Lesson 7: Right Triangles and Trig Test

A triangle has side lengths of 34 in, 20 in, and 47 in. Is the triangle acute, obtuse, or right?

In triangle ABC, if A is a right angle and MB is 45 degrees, what is the value of the opposite side?

If quilt squares are cut on the diagonal to form triangular pieces with a hypotenuse of 18 in, what is the side length of each piece?

Find the missing value to the nearest hundredth. sin____________=8/15

Find the missing value to the nearest hundredth. cos_________=9/20

Viola drives 200 meters up a hill that makes an angle of 9° with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?

The students in Mr. Collin's class measured the angle to the top of a building from their location. If they measured a distance from the base of the building of 154 ft, what is the distance?

An airplane pilot sights an atoll at an angle of depression of 5°. Given the horizontal distance from the airplane to the atoll is 4,629 meters, what is the vertical distance?

To find the height of a pole, a surveyor measures from 160 feet away and the angle of elevation is 62°. To the nearest foot, what is the height of the pole?

The length of the hypotenuse of a 30°-60°-90° triangle is 12. What is the perimeter?

Right Triangles and Trigonometry Overview

Triangle with side lengths 34 in, 20 in, 47 in is classified as obtuse.
In triangle ABC, with a right angle at A and angle B measuring 45 degrees, one side length is 14√2 ft.
The diagonal hypotenuse of triangular quilt pieces measures 18 in, leading to a side length of 9√2 in.

Trigonometric Values

To find missing values using sine, sin = 8/15 results in an angle of approximately 32.23°.
For cosine, cos = 9/20 yields a value of about 63.26°.

Application of Angles in Real Situations

Viola drives 200 meters at a 9° incline, covering a horizontal distance of approximately 197.5 in.
The distance to the top of a building measured from Mr. Collin's class is determined to be 154 ft.
An airplane pilot observes an atoll at a 5° angle of depression; the horizontal distance to the atoll is 4,629 meters.

Height and Distance Calculations

A surveyor measures 160 ft from a pole base and calculates the height to be approximately 307 ft using a 62° angle of elevation.
The hypotenuse of a 30°-60°-90° triangle measuring 12 leads to a perimeter formula of 18 + 6√3.

Additional Measurements

An unspecified measurement has been recorded as 27.8 in.
Another angle measures 42°.
One calculated distance is 454 miles.
An angle related value is 48.6°.
A final angle measurement found is 31°.

This quiz covers concepts related to right triangles and trigonometry, focusing on identifying triangle types and calculating side lengths. Utilize flashcards to reinforce your understanding of triangle properties, angles, and applications. Perfect for students preparing for a unit test on this topic.