Question

Please give the correct answer and explain im really trying to learn this so I need the explanation not just an answer. Thankyou!

Answer 1

Answer:

x = tan⁻¹(⅘)

Step-by-step explanation:

We can solve for x by using trigonometric ratios (sin, cos, and tan)

We need to apply the appropriate ratio that uses the two sides 8 and 10 from the perspective of x. See attached image for information about ratios. (Source: Math is Fun)

The tangent ratio is opposite divided by adjacent. It will relate x to the two sides. So we would write

tan(x) = ⁸⁄₁₀

Then we simplify and move the tan to the other side by multiplying both sides by the inverse of tan (since you cannot divide by tan)

tan(x) = ⅘

x = tan⁻¹(⅘)

Then we can use a calculator to evaluate x

If you want to find y, now that you have two angles of the triangle, you can find the sum of 90 + x and subtract that from 180 (since all angles of a triangle add up to 180) to find y.