1. Chapter 7 – Right Triangles and Trigonometry
Final Exam Review
Chapter 7 – Right Triangles and Trigonometry
Geometry
Ms. Rinaldi

2. Pythagorean Theorem
a2 + b2 = c2

3. Converse of the Pythagorean Theorem
If…
a2 + b2 = c2 then right
a2 + b2 < c2 then obtuse
a2 + b2 > c2 then acute

4. 45°-45°-90° Triangles The hypotenuse is times as long as each leg.
Hypotenuse = leg·

5. 30°-60°-90° Triangles
The hypotenuse is twice as long as the shorter leg.
The longer leg is times as long as the shorter leg.
Hypotenuse = 2·shorter leg
Longer leg = shorter leg·

6. Trigonometric Ratios
SOH CAH TOA

7. EXAMPLE
Solve a right triangle
Solve the right triangle. Round decimal answers to the nearest tenth.
SOLUTION
STEP 1
Find m B by using the Triangle Sum Theorem.
180o
= 90o + 42o + m B
48o
= m B

8. Solve a right triangle (continued)
EXAMPLE
Solve a right triangle (continued)
STEP 2
Approximate BC by using a tangent ratio.
tan 42o =
BC70
Write ratio for tangent of 42o.
70 tan 42o
= BC
Multiply each side by 70. BC
Approximate tan 42o 63 BC
Simplify and round answer.

9. Solve a right triangle (continued)
EXAMPLE
Solve a right triangle (continued)
STEP 3
Approximate AB by using a cosine ratio.
cos 42o =
70 AB
Write ratio for cosine of 42o.
AB cos 42o =
Multiply each side by AB. AB
cos 42o =
Divide each side by cos 42o. AB
Use a calculator to find cos 42o. AB
94.2
Simplify .
ANSWER
The angle measures are 42o, 48o, and 90o. The
side lengths are 70 feet, about 63 feet, and about 94 feet.