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3 years ago

15

The measure of one of the acute angles in a right triangle is five times the measure of the other acute angle. what is the measu

re of the smaller acute angle?

1 answer:

dusya [7]3 years ago

8 0

The measure of the smaller angle is 15°

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Alex

Answer:

The correct option is C ) 109.5°

Therefore,

$m\angle E=109.5\°$

Step-by-step explanation:

Given:

In Triangle DEF

d = 10

e = 18

f = 12

To Find

angle E = ?

Solution:

In Triangle DEF , Cosine Rule says

$\cos E=\dfrac{f^{2}+d^{2}-e^{2}}{2fd}$

Substituting the values we get

$\cos E=\dfrac{12^{2}+10^{2}-18^{2}}{2\times 12\times 10}$

$\cos E=\dfrac{-80}{240}=-\dfrac{1}{3}$

Therefore,

$\angle E=\cos^{-1}(-0.3333)$

$m\angle E=109.5\°$ ............As it is in Second Quadrant

Therefore,

$m\angle E=109.5\°$

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Step-by-step explanation:

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Hope this helps! :)
~Zain

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