Solving Right Triangle Problems

Solving Right Triangle Problems

->Students will be able to write the correct trig. ratio (G.SRT.6) and solve right triangle problems (G.SRT.8),

Solving Special Right Triangles In Spanish

• https://es.khanacademy.org/math/math2/xe2ae2386aa2e13d6:trig/xe2ae2386aa2e13d6:special-right-tri/v/45-45-90-triangles

• https://es.khanacademy.org/math/math2/xe2ae2386aa2e13d6:trig/xe2ae2386aa2e13d6:special-right-tri/v/intro-to-30-60-90-triangles

Multiple Choice

Find the value of y.

• 7
• 7√3
• 14√3
• (14√3)/3

Multiple Choice

Find the value of y to the nearest tenth.

• 4.5
• 3.2
• 2.3
• 5

Multiple Choice

Find the value of y.

• 11√2
• 11
• 22
• (11√2)/2

Multiple Choice

Find the value of y.

• 8
• 4
• 2√3
• 8√3

Multiple Choice

Find the value of y.

• 9
• 18√2
• 9√2
• (9√2)/2

Multiple Choice

Find a.

• 2√3
• 2
• 12
• 6

How to write a Trig Ratio:

-> Introduction to complementary trig (Sin/Cos G.SRT.7)

How to Write a Trig Ratio: Spanish

• https://es.khanacademy.org/math/math2/xe2ae2386aa2e13d6:trig/xe2ae2386aa2e13d6:trig-ratios-intro/v/basic-trigonometry

Multiple Choice

Which one is the easy way to remember trigonometric ratios?

• Sah Coh Toa
• Soh Cah Toa
• Soh Cah Tao
• Soh Ceh Toa

Multiple Choice

What is the ratio for Tangent

• $\frac{opp}{hyp}$

• $\frac{adj}{opp}$

• $\frac{opp}{adj}$

• $\frac{hyp}{opp}$

Multiple Choice

What is the ratio for Sine?

• $\frac{hyp}{opp}$

• $\frac{opp}{hyp}$

• $\frac{opp}{adj}$

• $\frac{adj}{opp}$

Multiple Choice

Select the correct ratio for SinA

• $\frac{37}{35}$

• $\frac{12}{35}$

• $\frac{35}{37}$

• $\frac{12}{37}$

Multiple Choice

What is the ratio for Cosine?

• $\frac{opp}{hyp}$

• $\frac{opp}{adj}$

• $\frac{adj}{opp}$

• $\frac{adj}{hyp}$

Multiple Choice

Find CosZ as a decimal rounded the the nearest tenth.

• 0.6

• 0.8

• 0.75

• 1.33

Multiple Choice

• $\frac{3}{4}$

• $\frac{3}{5}$

• $\frac{5}{4}$

• $\frac{5}{3}$

Multiple Choice

Set up the problem so that you can solve for X.

• sin X = 41/28
• tan X = 41/28
• cos X = 28/41
• sin X = 28/41

Pythagorean Theorem: Española

• https://es.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem

Multiple Choice

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet
• 26 feet
• 27 feet
• 28 feet

Multiple Select

Which equation can be used to solve the word problem: the diagonal of a t.v. is 40 inches and the height is 30. How wide is the t.v.? Check all that apply

• 30² + 40² = c²

• a² + 40² = 30²

• 30² + b² = 40²

• 40² + 30² = c²

• a² + 30² = 40²

Multiple Select

Based on the diagram, choose all the statements that are true.

Multiple Choice

Alan made a small four-sided table for his office.  The opposite sides of the table are 27 inches long and 36 inches long.  If the diagonal of the table measures 40 inches, does the table have right angles at the corners?  Why or why not?

• Yes, because it's a rectangle and rectangles have 90 degree angles in the corners
• Yes, because 27 and 36 are less than 40
• No, because 27²+36² does not equal 40²
• No, because 27+36 does not equal 40

Multiple Choice

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

Multiple Choice

Isabella has sticks that are 10cm, 11cm, and 13cm long.  Can she place the sticks together to form a right triangle?  Justify your answer.

• No, because 10+11 does not equal 13
• No, because 100+121 does not equal 169
• Yes, because there is a small side, medium side and long side
• Yes, because a triangle has 3 sides

Solving For a angle Using Trigonmetry: Spanish

• Notes: https://es.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle

Multiple Choice

A building 62 feet tall casts a shadow 21 meters long.  At what angle is the sun shining on the building?

• 19.80
• 18.71
• 70.20
• 71.29

Multiple Choice

Solve for the missing angle

• 50.5 degrees

• 12.7 degrees

• 36.9 degrees

• 72.2 degrees

Multiple Choice

Set up an equation that could be used to solve for the variable.

Multiple Choice

Which tool would you use?

• 45-45-90

• Pythagorean Theorem

• Triangle Angle Sum

• 30-60-90

Multiple Choice

Which tool would you use?

• Sine

• Cosine

• Tangent

• Pythagorean Theorem

Multiple Choice

Which tool would you use?

• Cos^-1

• Cosine

• Tangent

• Pythagorean Theorem

• Tan^-1

Multiple Choice

Example 2: Find, to the nearest degree, the angle which the sun's rays make with the ground when a flagpole 40 feet high casts a shadow 30 feet long.

• 48^o

• 37^o

• 28^o

• 53^o

Solving for a Side Using SOHCAHTOA Spanish

• https://es.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle

Multiple Choice

Which would you use to solve for the missing piece?

• $16^2+x^2=70^2$

• $\sin70\degree=\frac{16}{x}$

• $\cos70\degree=\frac{x}{16}$

• $\tan70\degree=\frac{x}{16}$

Multiple Choice

Which would you use to solve for the missing piece?

•  $4+3+x=180$  

•  $4^2+3^2=x^2$  

•  $x^2+3^2=4^2$  

•  $x=3\ \left(45-45-90\right)$  

Multiple Choice

Solve for x. Round to the nearest tenth.

• 25.7
• 35.4
• 6.4
• 5.6

Multiple Choice

Solve for x. Round to the nearest tenth.

• 11.1
• 9.3
• 13.0
• 5.5

Multiple Choice

Which trigonometric function would you use to find "h", the height of the tree?

• sine

• cosine

• tangent

• none of these

Multiple Choice

Solve for the misssing distance

• 18.9 meters
• 19.5 meters
• 47.2 meters
• 27.5 meters

Multiple Choice

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree.  The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse? 

• 7.5 ft 
• 15 ft 
• 26 ft 
• 30 ft 

Multiple Choice

Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 

• 63 ft
• 65 ft
• 74 ft
• 87 ft

Multiple Choice

Solve the right triangle.

• <B = 39^o, AB = 11.58, AC = 7.29
• <B = 39^o, AB = 7.29, AC = 11.58
• <B = 129^o, AB = 11.58, AC = 7.29
• <B = 129^o, AB = 7.29, AC = 11.58

Multiple Choice

From the top of a canyon, the angle of depression to the far side of the river is 52°. The angle of depression to the near side of the river is 79°. The depth of the canyon is 400 feet. To the nearest foot, how wide is the river at the bottom of the canyon?

• 104 ft

• 235 ft

• 204 ft

• 785 ft

Multiple Choice

Jose would like to know the height of the brick building shown in the picture, if the angle of elevation is 50 degrees and he is 36 feet from the building.  Which of these is the calculator ready expression to find the building height?

• 36 Sin (50)
• 36 Tan (50)
• 36 Sin (50) + 6
• 36 Tan (50) + 6