EOC Review: Trigonometry Real World

What is the sine ratio of ∠𝑃 in the given triangle?

A 30-foot long escalator forms a 41° angle at the second floor. Which is the closest height of the first floor?

• 20 feet

• 22.6 feet

• 24.5 feet

• 26 feet

Find the measure of the missing angle. Round to the nearest degree. 

• 49^o
• 50^o
• 41^o
• 33^o

Solve for the missing distance.

• 18.9
• 19.5
• 47.3
• 27.5

Solve for the missing angle. Round the nearest degree.

• 50

• 36

• 37

• 35

As shown in the diagram, the angle of elevation from a point on the ground to the top of the tree is 34°.

If the point is 20 feet from the base of the tree, what is the height of the tree, to the nearest tenth of a foot?

Mathematical Equivalence

ON

In Δ𝐴𝐵𝐶, the complement of ∠𝐵 is ∠𝐴. Which statement is always true?

• 𝑡𝑎𝑛 ∠𝐴 = 𝑡𝑎𝑛 ∠𝐵

• 𝑠𝑖𝑛 ∠𝐴 = 𝑠𝑖𝑛 ∠𝐵

• 𝑐𝑜𝑠∠𝐴 =𝑡𝑎𝑛 ∠𝐵

• 𝑠𝑖𝑛 ∠𝐴 =𝑐𝑜𝑠 ∠𝐵

Answer explanation

Remember that the sine of one angle is equal to the cosine of the other angle (its complement) in a right triangle. Their ratios will be the same!

The diagram shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures 11.75 feet from the ground to the top of the loading platform.

Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground.

Mathematical Equivalence

ON

Jane and Mark each build ramps to jump their remote-controlled cars.

Both ramps are right triangles when viewed from the side. The incline of Jane's ramp makes a 30-degree angle with

the ground, and the length of the inclined ramp is 14 inches. The incline of Mark's ramp makes a 45-degree angle

with the ground, and the length of the inclined ramp is 10 inches.

a) What is the horizontal length of the base of Jane's ramp and the base of Mark's ramp?

b) Which car is launched from the highest point?

• 12.12 in & 7.07 in;

  Mark's car

• 12.12 in & 7.07 in;

  Jane's car

• 20 in & 7 in;

  Mark's car

• 20 in & 7 in;

  Jane's car

In the figure, a pole has two wires attached to it, one on each side, forming two right triangles.

How tall is the pole in feet?

Answer to the nearest tenths place.

Mathematical Equivalence

ON