Question

Solve for m and n I been stuck on this question for an hour

Answer 1

Answer:

m = 10 , n = 5$\sqrt{2}$

Step-by-step explanation:

using the cosine and tangent ratio in the right triangle and the exact values

cos45° = $\frac{1}{\sqrt{2} }$ and tan45° = 1 , then

cos45° = $\frac{adjacent}{hypotenuse}$ = $\frac{5\sqrt{2} }{m}$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

m = 5$\sqrt{2}$ × $\sqrt{2}$ = 5 × 2 = 10

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tan45° = $\frac{opposite}{adjacent}$ = $\frac{n}{5\sqrt{2} }$ = 1 , then

n = 5$\sqrt{2}$