Geometry – Warm Up Right Triangles Day 8
Name _____________
Date _____________
Use the following diagram. Round decimals to the nearest tenth.
P
q
r
Q
p
R
1. If PR = 12 and m  R = 19° solve the right triangle.
GEOMETRY: Unit 7 (Chapter 7) Right Triangles
Unit Review
WHAT DO YOU NEED TO KNOW?
7.1 and 7.2 Apply Pythagorean Theorem and Use the Converse of Pythagorean Theorem
· Find unknown leg or hypotenuse
1. Find the length of the hypotenuse of the right triangle.
Trigonometry: 7.5 and 7.6
· What are the ratios for sine, cosine, and tangent?
(Hint: Remember SohCahToa)
· How can you find the sine, cosine, or tangent of a given angle?
1. Find sin B, cos B, and tan B. Write each answer as a fraction and as a decimal rounded to
four places.
· How can you use sine, cosine, and tangent to find the values of missing lengths of a triangle?
1. Basketball You walk from one corner of a basketball court to the opposite corner. The court
is 94 feet long and your diagonal path creates a 62° angle from the baseline. Use a
trigonometric ratio to calculate the distance you walk.
2. Roller Coaster You are at the top of a roller coaster 100 feet above the ground. The angle of
depression is 44°. About how far do you ride down the hill?
3. Railroad A railroad crossing arm that is 20 feet long is stuck with an angle of elevation of
35° Find the lengths x and y
4. Lighthouse Find the height h of the lighthouse to the nearest foot.
7.7 Solving a Right Triangle:
- What does it mean to “solve a right triangle”
· What information must we know to solve a triangle?
· What are the inverse trigonometric functions?
· How can we find the measure of a given angle given the sine, cosine and tangent of that angle?
Let A and B be acute angles in two right triangles. Use a calculator to approximate the
measures of A and B to the nearest tenth of a degree.
1. sin A = 0.76
2. cos B = 0.17
· How can we use inverse trigonometric ratios to find the missing angles of a triangle?
1. In Example 1 solve the right triangle:
2. Model Train You are building a track for a model train. You want the track to incline from
the first level to the second level, 4 inches higher, in 96 inches. Is the angle of elevation
less than 3°?
3. Solve the right triangle. Round decimal answers to the nearest tenth.
4. Solve the right triangle. (find EVERYTHING!) Round answers to the nearest tenth.
P
20
R
14
Q