Question

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x. Which is the best approximation for the measure of angle ABC? 27.7° 31.7° 58.3° 62.3°

Answer 1

The best approximation for the measure of angle ABC is 58.3° ⇒ 3rd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

• $sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
• $cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
• $tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠ABC is BC

∵ AB = 20 centimeters

∵ BC = 10.5 centimeters

- Use cosine ratio to find the measure of the angle because you

   have the adjacent side of the angle ABC and the hypotenuse

∵ m∠ABC is x

∵ $cos(x)=\frac{BC}{AB}$

∴ $cos(x)=\frac{10.5}{20}$

- To find x use the inverse of cos(x)

∵ $x=cos^{-1}(\frac{10.5}{20})$

∴ x = 58.33°

∴ m∠ABC = 58.33°

The best approximation for the measure of angle ABC is 58.3°

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

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Answer 2

Answer:

C

Step-by-step explanation:

I took the test on E2020.