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8.7: Chapter 8 Review

Difficulty Level: At Grade Created by: CK-12

Keywords & Theorems

The Pythagorean Theorem

  • Pythagorean Theorem
  • Pythagorean Triple
  • Distance Formula

The Pythagorean Theorem Converse

  • Pythagorean Theorem Converse
  • Theorem 8-3
  • Theorem 8-4

Similar Right Triangles

  • Theorem 8-5
  • Geometric Mean

Special Right Triangles

  • Isosceles Right (45-45-90) Triangle
  • 30-60-90 Triangle
  • 45-45-90 Theorem
  • 30-60-90 Theorem

Tangent, Sine and Cosine Ratios

  • Trigonometry
  • Adjacent (Leg)
  • Opposite (Leg)
  • Sine Ratio
  • Cosine Ratio
  • Tangent Ratio
  • Angle of Depression
  • Angle of Elevation

Solving Right Triangles

  • Inverse Tangent
  • Inverse Sine
  • Inverse Cosine

Review

Fill in the blanks using right triangle \begin{align*}\triangle ABC\end{align*}ABC.

  1. \begin{align*}a^2 + \underline{\; \; \; \; \; \; \; \;} ^2 = c^2\end{align*}a2+2=c2
  2. \begin{align*}\sin \underline{\; \; \; \; \; \; \; \;} = \frac{b}{c}\end{align*}sin=bc
  3. \begin{align*}\tan \underline{\; \; \; \; \; \; \; \;} = \frac{f}{d}\end{align*}tan=fd
  4. \begin{align*}\cos \underline{\; \; \; \; \; \; \; \;} = \frac{b}{c}\end{align*}cos=bc
  5. \begin{align*}\tan^{-1} \left( \frac{f}{e} \right ) = \underline{\; \; \; \; \; \; \; \;}\end{align*}tan1(fe)=
  6. \begin{align*}\sin^{-1} \left( \frac{f}{b} \right) = \underline{\; \; \; \; \; \; \; \;}\end{align*}sin1(fb)=
  7. \begin{align*}\underline{\; \; \; \; \; \; \; \;} ^2 + d^2 = b^2\end{align*}2+d2=b2
  8. \begin{align*}\frac{?}{b} = \frac{b}{c}\end{align*}?b=bc
  9. \begin{align*}\frac{e}{?} = \frac{?}{c}\end{align*}e?=?c
  10. \begin{align*}\frac{d}{f} = \frac{f}{?}\end{align*}df=f?

Solve the following right triangles using the Pythagorean Theorem, the trigonometric ratios, and the inverse trigonometric ratios. When possible, simplify the radical. If not, round all decimal answers to the nearest tenth.

Determine if the following lengths make an acute, right, or obtuse triangle. If they make a right triangle, determine if the lengths are a Pythagorean triple.

  1. 11, 12, 13
  2. 16, 30, 34
  3. 20, 25, 42
  4. \begin{align*}10 \sqrt{6}, 30, 10 \sqrt{15}\end{align*}106,30,1015
  5. 22, 25, 31
  6. 47, 27, 35

Find the value of \begin{align*}x\end{align*}x.

  1. The angle of elevation from the base of a mountain to its peak is \begin{align*}76^\circ\end{align*}76. If its height is 2500 feet, what is the length to reach the top? Round the answer to the nearest tenth.
  2. Taylor is taking an aerial tour of San Francisco in a helicopter. He spots AT&T Park (baseball stadium) at a horizontal distance of 850 feet and down (vertical) 475 feet. What is the angle of depression from the helicopter to the park? Round the answer to the nearest tenth.

Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9693.

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CK.MAT.ENG.SE.1.Geometry-Basic.8.7