Question

WORK OUT ASAP PLEASE

The diagram shows a right-angled triangle.
80%
10cm
Х°
21cm
Find the size of angle x.
Give your answer correct to 1 decimal place.

Answer 1

x = 25.5°

Explanation:

First find the hypotenuse of the right triangle given by the formula

`c = \sqrt{a^(2) + b^(2)}`

where c is the hypotenuse and a, b the two sides

Let's call the vertical leg as a and the horizontal leg as b

Then we have a = 10, b = 21

So

`c = \sqrt{10^(2) + 21^(2)}\\\\c = √(100 + 441)\\\\c = √(541)\\\\c = 23.2594\\\\\\`

By the law of sines, the ratios of the sides of a triangle to the sine of the angles opposite must be the same. The hypotenuse is opposite the 90° angle. and the side of length 10 is opposite angle x

So

`(23.2594)/(\sin 90) = (10)/(\sin x)`

But sin 90 = 1. So the above equation reduces to

`2.2594 = (10)/(\sin x)\\\\\\\implies \sin x = (10)/(23.2594)\\\\\implies \sin x = 0.43\\\\\\\\x = sin ^(-1)(0.43) = 25.4675\\\\`

Rounded to 1 decimal place
x = 25.5°

Answer 2

x° ≈ 25.5°

Explanation:

The relationship between the two given sides and angle x are Opposite and Adjacent. So we'll use tan(x) = 10/21 to start.

Take the Inverse tan (tan⁻¹) to find x: x = tan⁻¹(10/21) ==> calculator