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2 years ago

If one acute angle of a right triangle measure 37 what's the measure of the other acute angle

Mathematics

1 answer:

Ghella [55]2 years ago

5 0

53°

Step-by-step:

- All angles in a triangle add up to 180°.

- Since your triangle is a right angle triangle, one of the angles are 90°.

- You already know another one, 37°.

- All you have to do to find the last one is to subtract the two you already know from 180.

180 - (90+37)

= 180 - 127

= 53

The measure of the last angle is 53°.

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Given:

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Solution:

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Opposite side to θ = ?

Using Pythagoras theorem:

$\text {Hypotenuse}^2 = \text{adjacent}^2+\text{opposite}^2$

$18^2 =10^2+\text{opposite}^2$

$324=100+\text{opposite}^2$

Subtract 100 from both sides.

$224=\text{opposite}^2$

Taking square root on both sides.

$4\sqrt{14}=\text{opposite}$

Using trigonometric ratio formula:

$$\sin\theta =\frac{\text{opposite }}{\text{hypotenuse}}$

$$\sin\theta =\frac{4\sqrt{14} }{18}$

$$\csc\theta =\frac{\text{hypotenuse}}{\text{opposite }}$

$$\csc\theta =\frac{18}{4\sqrt{14} }$

$$\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }}$

$$\cos \theta=\frac{10}{18}$

$$\sec \theta=\frac{\text { hypotenuse }}{\text { adjacent side }}$

$$\sec \theta=\frac{18 }{10}$

$$\tan \theta=\frac{\text { opposite side }}{\text { adjacent side }}$

$$\tan \theta=\frac{4\sqrt{14} }{10}$

$$\cot \theta=\frac{\text { adjacent side }}{\text { opposite side }}$

$$\cot \theta=\frac{10}{4\sqrt{14} }$

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Using inequality for the give interval which states that :
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oksano4ka [1.4K]

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Galina-37 [17]

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