Question 1

Use special right triangle ratios to find the length of the hypotenuse.14594515O A. 153B. 15

Use special right triangle ratios to find the length of the hypotenuse.14594515O A-example-1

Question 2

Using the trigonometry ratio that states that

$\begin{gathered} \sin \theta\text{ = }\frac{opp}{\text{hyp}},\text{ cos }\theta\text{ = }\frac{\text{adj}}{\text{hyp}},\text{ and tan }\theta\text{ = }\frac{opp}{\text{adj}} \\ \text{From the diagram given, 15 is the adjacent side. The logest side of the triangle is the hypotenuse and the other side is the opposite side} \\ So\text{ we will apply cos }\theta\text{ = }\frac{\text{adj}}{\text{hyp}},\text{ since we are looking for the hypotenuse and the adjacent is given.} \\ So,\text{ from cos }\theta\text{ = }\frac{\text{adj}}{\text{hyp}}\text{ note that }\theta\text{ is the acute angle 45} \\ \text{ cos 45 = }\frac{15}{\text{hyp}} \\ \text{cross multiplying, } \\ \cos \text{ 45 hyp = 15} \\ \text{hyp = }\frac{15}{\cos\text{ 45}} \\ \text{hyp = }\frac{15}{\frac{\sqrt[]{2}}{2}}\text{ rationalizing the denominator, we get } \\ \text{hyp = }15\sqrt[]{2} \\ \text{Answer is option D} \end{gathered}$

Therefore, the answer is OPTION D

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