Question

HELP FAST GIVE A DECENT AMOUNT OF POINTS! FOR EASY!

Answer 1

Answer:

The value of angle is 56.9°

Step-by-step explanation:

First, you have to find the length of hypotenuse using Pythagoras' Theorem, c² = a² + b² :

${c}^{2} = {a}^{2} + {b}^{2}$

$let \: a = 8.25 \\ let \: b = 6.45$

${c}^{2} = {8.25}^{2} + {6.45}^{2}$

${c}^{2} = 68.0625 + 41.6025$

${c}^{2} = 109.665$

$c = \sqrt{109.665}$

$c = 10.47cm \: (4s.f)$

In order to find θ, you have to apply Sine Rule :

$\sin(θ) = \frac{opposite}{adjacent}$

$let \: oppo. = 8.77 \\ let \: hypo. = 10.47$

$\sin(θ) = \frac{8.77}{10.47}$

$θ = { \sin( \frac{8.77}{10.47} ) }^{ - 1}$

$θ = 56.9 \: (1d.p)$