Respuesta :

calculista

Answer:

The value of x is 15°

Step-by-step explanation:

we know that

If in a right triangle (A and B are the acute angles)

sin(A)=cos(B)

then

angle A and angle B are complementary angles

so

A+B=90°

therefore

In this problem

sin(2x+14)°=cos(46°)

(2x+14)°+46°=90°

Solve for x

2x+60°=90°

2x=30°

x=15°

ashishdwivedilVT

The value of acute angle x in the given right triangle is 15°.

As we know that

cosα = sin(90-α)......(1)

We can write the right-hand side of the given equation in sine form using equation (1)

What is an acute angle?

An acute angle is an angle that measures less than 90°

Given equation is

[tex]sin(2x+14) = cos 46\\\\sin(2x+14) = sin(90-46).....fromEQ1\\\\sin(2x+14) = sin 44\\\\2x+14 = 44\\\\2x = 30\\\\x = 15[/tex]

Therefore, the value of acute angle x in the given right triangle is 15°.

To get more about trigonometric identities visit:

https://brainly.com/question/24349828

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