Math 20-3 - Two or More Triangles

Which trigonometric ratio should you use?

• Tangent Ratio

• Sine Ratio

• Cosine Ratio

• Any ratio

Which trigonometric ratio should you use?

• Tangent Ratio

• Sine Ratio

• Cosine Ratio

• Any ratio

Which trigonometric ratio should you use?

• Tangent Ratio

• Sine Ratio

• Cosine Ratio

• Any ratio

Which side is opposite angle x?

• 1

• 2

• 3

Which side is the hypotenuse?

• 1

• 2

• 3

If the protruding part of the cabinet shelves was cut off, and triangles (rather of pentagons) were formed, the triangles would most likely be:

• A) right.
  

• B) obtuse.
  

• C) equilateral.

• D) similar, but not congruent.

Answer explanation

A right triangle is one with a 90° angle. The two walls of the cabinet most likely meet at 90° angle, leaving a right triangle.

An equilateral triangle is one where all three sides are the same (and all angles are 60°), and an obtuse triangle contains one angle that is greater than 90°.

Similar triangles are the same shape and congruent triangles are the same size.

A picture of a child on a slide is shown.

A right triangle is formed by:

• A) the ladder, the slide and the ground.

• B) the child's torso, his legs and a line connecting head to toes.

• C) the child's back, the ladder and a line connecting head to base of ladder.

• D) the ladder, the ground and a vertical line connecting the top of the slide and the ground.

Answer explanation

A right triangle is one with a 90° angle. The only description given that would yield a triangle with a 90° angle is Option D "the ladder, the ground and a vertical line connecting the top of the slide and the ground".

Which of the following statements about the diagram is true?

• A) The measure of z is greater than 47°.

• B) The length of x is greater than 1.4 km.

• C) The length of x is greater than the length of y.

• D) The measure of w is greater than the measure of z.

Answer explanation

The sum of the interior angles in a triangle is 180°.

In a right triangle, one angle is 90° and the sum of the other two is 90°.

As such, the measure of w is 90° – 22° = 68° and the measure of z is 90° – 47° = 43°.

Therefore, Option B is true; since 68° is greater than 43°.

A large tree, Tree 1, casts a shadow on the ground as shown in the diagram. Using the information in the diagram, if Tree 2 is halfway between the base of Tree 1 and the top of the shadow formed on the ground by Tree 1, what is the height of Tree 2?

• 10 m

• 14.36 m

• 28.72 m

• 17.5 m

Answer explanation

A person in a boat at sea looks upwards to the top of a tree, located on a cliff. The details of the boat's location is shown in the diagram :

Using this information, how far above sea level is the top of the tree?

• A) 49.33 m

• B) 212 m

• C) 99.03 m

• D) 49.70 m

Answer explanation