question 1-9 in △abc, m∠a = 90°. if cosb = 0.8, what is the value of si…

题目

question 1-9
in △abc, m∠a = 90°. if cosb = 0.8, what is the value of sinc to the nearest tenth?
enter the correct answer in the box.

解题步骤

Understand the question
question 1-9
in △abc, m∠a = 90°. if cosb = 0.8, what is the value of sinc to the nearest tenth?
enter the correct answer in the box.
Explanation
Step1: Analyze triangle angles

In right triangle $ \triangle ABC $ with $ \angle A = 90^\circ $, we know that $ \angle B + \angle C=90^\circ $ (since the sum of angles in a triangle is $ 180^\circ $ and $ \angle A = 90^\circ $). So $ \angle C = 90^\circ-\angle B $.

Step2: Use trigonometric co-function identity

We use the co - function identity $ \sin(90^\circ - x)=\cos(x) $. Let $ x = \angle B $, then $ \sin C=\sin(90^\circ - B)=\cos B $.

Step3: Substitute the given value

We are given that $ \cos B = 0.8 $, so from the above identity, $ \sin C=\cos B = 0.8 $.
Final answer
$ 0.8 $

答案

Explanation

Step1: Analyze triangle angles

In right triangle $ \triangle ABC $ with $ \angle A = 90^\circ $, we know that $ \angle B + \angle C=90^\circ $ (since the sum of angles in a triangle is $ 180^\circ $ and $ \angle A = 90^\circ $). So $ \angle C = 90^\circ-\angle B $.

Step2: Use trigonometric co-function identity

We use the co - function identity $ \sin(90^\circ - x)=\cos(x) $. Let $ x = \angle B $, then $ \sin C=\sin(90^\circ - B)=\cos B $.

Step3: Substitute the given value

We are given that $ \cos B = 0.8 $, so from the above identity, $ \sin C=\cos B = 0.8 $.

Answer

$ 0.8 $

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Question Analysis

Subject mathematics

Sub Subject geometry

Education Level high school

Difficulty unspecified

Question Type calculation

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-01-30T12:08:51

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question 1-9
in △abc, m∠a = 90°. if cosb = 0.8, what is the value of sinc to the nearest tenth?
enter the correct answer in the box.

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