Question

Find the measure of x. 8 62° X x = [?]​

Answer 1

Assuming triangle ABC, where angle A is 62 degrees, angle B is 90 degrees, side AB is 8 units, the length of side AC (denoted as x) is approximately 7.06 units.

In a triangle, the sum of all angles is always 180 degrees. Given that angle A is 62 degrees and angle B is 90 degrees, you can find angle C by subtracting the sum of angles A and B from 180:

Angle C = 180 − Angle A − Angle B

Angle C = 180 − 62 − 90

Angle C = 28

Now, in a right-angled triangle (which triangle ABC is since angle B is 90 degrees), the two non-right angles (in this case, angles A and C) are complementary, meaning they add up to 90 degrees. So, angle C is also 90 - 28 = 62 degrees.

Now that we know all three angles of triangle ABC, we can use the Law of Sines to find the length of side AC (denoted as x)

The Law of Sines states:

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

In this case, let a=BC, b=AC, and c=AB.

Also, let A=∠A, B=∠B, and C=∠C

`(8)/(\sin 90^(\circ))=(x)/(\sin 62^(\circ))`

Since
`\sin 90^(\circ)=1`, the equation simplifies to:

`8=(x)/(\sin 62^(\circ))`

To solve for x, multiply both sides by
`\sin 62^(\circ)`:

`x=8 \cdot \sin 62^(\circ)`

Now, you can calculate

`\begin{aligned}& x \approx 8 \cdot 0.88295 \\& x \approx 7.0636\end{aligned}`

So, the length of side AC (denoted as x) is approximately 7.06 units.

Answer 2

x ≈ 17

Explanation:

using the cosine ratio in the right triangle

cos62° =
`(adjacent)/(hypotenuse)` =
`(8)/(x)` ( multiply both sides by x )

x × cos62° = 8 ( divide both sides by cos62° )

x =
`(8)/(cos62)` ≈ 17 ( to the nearest whole number )