1 Answer

Caleb Brinkman · Answer 1 · 2021-02-11T00:00:01+0000

Answer:

The value of angle is 56.9°

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 = √(109.665)

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

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

$\sin(θ) = (opposite)/(adjacent)$

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

$\sin(θ) = (8.77)/(10.47)$

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

$θ = 56.9 \: (1d.p)$

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