Question

Solve for x. Round to the nearest tenth of a degree, if necessary.

Answer 1

`x = 59.16 \degree`

Explanation:

We are given a right angled triangle, with two sides as 4.9 and 8 . And we are interested in finding out the measure of the angle "x" . With respect to angle x , the side measuring 8 is perpendicular and that measuring 4.9 is base.

In a right angled triangle, tangent is defined as the ratio of perpendicular and base .

So , according to the question,

• p = 8
• b = 4.9

Now we have;

`\implies \tan\theta =(p)/(b) \\`

Here the angle is " x " , so that ,

`\implies \tan x =(8)/(4.9)\\`

Simplify,

`\implies \tan x = 1.63 \\`

Take arctan on both the sides,

`\implies \arctan (\tan x ) = \arctan(1.63) \\`

Simplify,

`\implies x = \arctan(1.63)\\`

`\implies \underline{\underline{ x = 59.16\degree \approx 59.2\degree}}\\`

Hence the value of x is 59.2° .

Answer 2

x ≈ 58.5°

Explanation:

using the tangent ratio in the right triangle

tan x =
`(opposite)/(adjacent)` =
`(DE)/(EF)` =
`(8)/(4.9)` , then

x =
`tan^(-1)` (
`(8)/(4.9)` ) ≈ 58.5° ( to the nearest tenth )