For the acute angles in a right triangle, . What is the value of
? (1 point)

Ask by Gray Goodwin. in the United States

Jan 23,2025

Question

For the acute angles in a right triangle, $$ \sin \left(3 x+10^{\circ}\right)=\cos \left(x+24^{\circ}\right) $$. What is the value of $$ x $$ ? (1 point)

UpStudy AI · Accepted Answer

Let's solve the equation:

$$
\sin(3x + 10^\circ) = \cos(x + 24^\circ)
$$

We know that $$\sin(A) = \cos(90^\circ - A)$$. Therefore:

$$
3x + 10^\circ = 90^\circ - (x + 24^\circ)
$$

Simplifying:

$$
3x + 10^\circ = 66^\circ - x
$$
$$
4x = 56^\circ
$$
$$
x = 14^\circ
$$

**Answer:** $$14^\circ$$
$$ x = 14^\circ $$

For the acute angles in a right triangle, . What is the value of
? (1 point)

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For the acute angles in a right triangle, . What is the value of ? (1 point)