Question

For questions 6 – 10, find the unknown side length. number 10

Answer 1

Answer: $\begin{gathered} s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \\ s\text{ = 14.142 \lparen decimal approx.\rparen} \end{gathered}$

Explanation:

10) Given:

hypotenuse = 20

angle = 45°

To find:

length of s

angle = 45

opposite = side opposite the angle = s

To find the value of s, w will apply sine ratio (SOH)

$sin\text{ 45 = }\frac{opposite}{hypotenuse}$$\begin{gathered} sin\text{ 45 = }\frac{s}{20} \\ s\text{ = 20sin45} \\ sin\text{ 45 = }\frac{\sqrt{2}}{2} \\ \\ s\text{ = 20}\times\frac{\sqrt{2}}{2} \\ s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \end{gathered}$$\begin{gathered} s\text{ = 20sin45} \\ s\text{ = 20\lparen0.7071\rparen} \\ s\text{ = 14.142 \lparen decimal approximation\rparen} \end{gathered}$