# Section 4.3 – Right Triangle Trigonometry

Section Details.
• Right triangle definitions of trigonometric functions
• Solving for trigonometric functions of an angle when given some information about the angle
• Special right triangles and using them to evaluate the trigonometric functions for common angles
• Reciprocal, Quotient, and Pythagorean Trigonometric Identities
• Using right triangles to solve word problems

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.
1. Find the exact value of the six trigonometric functions, given the following:
hypotenuse = 29,  side opposite the angle = 21

$$\sin\theta=\dfrac{21}{29}$$
$$\cos\theta=\dfrac{20}{29}$$
$$\tan\theta=\dfrac{20}{21}$$
$$\sec\theta=\dfrac{29}{20}$$
$$\csc\theta=\dfrac{29}{21}$$
$$\cot\theta=\dfrac{21}{20}$$

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2. Given $$\sin\theta=\cfrac{4}{7}$$ and $$\theta$$ in Q1, use the trigonometric identities to find the exact value of each:
1. ​$$\displaystyle{ \cos (\theta)}$$
2. $$\displaystyle{ \cot (\theta)}$$
3. $$\csc (\theta)$$
4. $$\tan(90^{\circ} - \theta)$$​

1. $$\cos\theta=\dfrac{\sqrt{33}}{7}$$
2. $$\cot\theta=\dfrac{\sqrt{33}}{4}$$
3. $$\csc\theta=\dfrac{7}{4}$$
4. $$\tan(90^\circ-\theta)=\dfrac{\sqrt{33}}{4}$$

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3. From a point on the ground 47 feet from the foot of a tree, the angle of elevation of the top of the tree is $$30^\circ$$. Find the height of the tree.

$$\dfrac{47}{\sqrt{3}}$$ ft

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4. Find the exact value of $$x$$ and $$y$$.

$$x=\dfrac{70}{\sqrt{2}}$$, $$y=\dfrac{70}{\sqrt{2}}$$

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