Question

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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.

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:

\( 0.8 \)