# Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set: 66

$\sin A$ = 0.600 $\\cos A$ = 0.800 $\sin B$ = 0.800 $\cos B$ = 0.600

#### Work Step by Step

Steps to Answer- We will use given data about triangle ABC & Pythagoras Theorem to solve for 'b'- We know that - $c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem) Therefore - $b^{2} =c^{2} - a^{2}$ $b^{2} = (5.70)^{2} - (3.42)^{2}$ $b^{2} = 32.4900 - 11.6964$ $b^{2} = 20.7936$ therefore $b = \sqrt (20.7936)$ b = 4.56 Now we can write the required T-functions of A and B using $a=3.42$ , b = 4.56 and c = 5.70 $\sin A = \frac{a}{c} = \frac{3.42}{5.70}$ = 0.600 $\\cos A = \frac{b}{c} = \frac{4.56}{5.70}$ = 0.800 $\sin B = \frac{b}{c} =\frac{4.56}{5.70}$ = 0.800 $\cos B =\frac{a}{c} = \frac{3.42}{5.70}$ = 0.600

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