Final answer:
To find the value of x in a right triangle with a hypotenuse of 46 and an angle of 70 degrees, use the cosine function. Calculate x by multiplying the cosine of 70 degrees with the hypotenuse length, resulting in x being approximately 15.73.
Step-by-step explanation:
To find the value of x in a right triangle where the hypotenuse is 46, the adjacent side is x, and the angle is 70 degrees, we can use the cosine function. The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse (cos(θ) = adjacent/hypotenuse). Therefore, we have:
cos(70°) = x/46
By multiplying both sides by 46 to solve for x, we get:
x = 46 × cos(70°)
Now, calculate the cosine of 70 degrees and multiply by 46:
x ≈ 46 × 0.3420 (using a calculator)
x ≈ 15.732
The value of x is approximately 15.73, which represents the length of the adjacent side to the angle in question.