Right Triangles

The Pythagorean Theorem

100

Do the following sides form a Pythagorean triple? √3, √4 and √5?

No

200

What kind of triangle has side lengths 5, 6, and 10?

An obtuse triangle

300

If a lamppost 12 feet tall creates a shadow 5 feet long what is the distance between the top of the lamppost and the part of the shadow farthest away from it?

13 feet

400

A right triangle has a leg length 6 and a hypotenuse length 10. What is the length of the other leg?

8

500

In a right triangle, the hypotenuse is 9 and one of the legs is 6. How long is the other leg? Your answer should be in simplified radical form.

3√5

45-45-90 Triangles

100

If 45-45-90 triangle has a hypotenuse of 4√2 then what is the length of one of the legs of that triangle?

4

200

What is the ratio of the sides of 45-45-90 Triangle? (Example - a: b: c)

1:1:√2

300

In a 45-45-90 triangle, one of the legs is √3. How long is the hypotenuse? Your answer should be in simplified radical form.

√6

400

In a 45-45-90 triangle, one of the legs is √51. How long is the other leg? Your answer should be in simplified radical form.

√51

500

If a right triangle has side lengths of 4,4 and 4√2 what type of right triangle is it?

45-45-90 Triangle OR Isoceles

30-60-90 Triangles

100

In a 30-60-90 triangle, the short leg is 1. How long is the long leg AND the hypotenuse? Your answer should be in simplified radical form.

Long leg is √3 Hypotenuse is 2

200

In a 30-60-90 triangle, the hypotenuse is 4. What is the length of the short leg? Your answer should be in simplified radical form.

2

300

What is the ratio of the sides of a 30-60-90 triangle? (Example - a: b: c)

1:2:√3

400

In a 30-60-90 triangle the long leg is √6. What is the length of the short leg?

√2

500

If the long leg of a 30-60-90 triangle is 6 what is the length of the hypotenuse AND the short leg?

Short leg is 2√3 Hypotenuse is 4√3

Trig Ratios

100

What acronym can you use to remember the three trigonometric ratios? Spelling counts.

SohCahToa

200

In a right triangle, the hypotenuse is 10. How long is the side across from the 32 degree angle? Round to the nearest tenth.

5.3

300

Which trigonometric ratio should you use if you know the opposite side and are trying to find the length of the adjacent side?

Tangent

400

What two sides of a triangle (in relation to a particular angle) are used for finding the cosine ratio?

adjacent side and the hypotenuse

500

In order to unload clay easily, the body of a dump truck must be elevated to at least 45°. The body of a dump truck that is 14 feet long has been raised 8 feet. Will the clay pour out easily? Explain your reasoning.

no; The body of the dump truck has only been elevated to about 34.8°, which is less than the recommended minimum angle of 45°. 

sin X = 8/14

Miscellaneous

100

Can you have an angle bigger than 90 degrees in a right triangle?

No

200

When do you use the inverse trigonometric functions?

When trying to find an angle.

300

Solve the equation: 12/x = 3/2

x = 8

400

Add the number of people who in Mrs. Tapper's immediate family to the number of stars on the American flag, and then divide that by the square root of 64. What number do you get?

7

500

While flying a kite, Linda lets out 45 feet of string and anchors it to the ground. She determines that the angle of elevation of the kite is 58 degrees. What is the height of the kite from the ground? Round to the nearest tenth.

38.2 feet