Question

Please help i really need this answer asap thankyou.

Work out the value of x.

Answer 1

33.7°

Explanation:

We know that both small triangles are right triangles, but we don't know that the large triangle is a right triangle.

1. Find the altitude of the large triangle.

a² + b² = c²

2.5² + b² = 5²

b² = 25 - 6.25

b² = 18.75

b = √18.75

The altitude of the large triangle is the opposite leg to angle x in the left small triangle. The adjacent leg to angle x is 6.5 cm.

tan x = opp/adj

tan x = √18.75/6.5

tan x = 0.6661733

x = tan^-1 0.6661733

x = 33.7

Answer: 33.7°

Answer 2

x =33.8°

Explanation:

First find the altitude of the ΔADC using Pythagorean theorem.

altitude² = hypotenuse² - base²

= 5² - 2.5²

= 25 - 6.25

= 18.75

altitude = √18.75

altitude = AD = 4.3 cm

Now, to find x, use tan ratio.

`\sf \boxed{\bf Tan \ x = (opposite \ side \ of \ \angle x)/(adjacent \ side \ of \ \angle x)}`

`\sf = (4.3)/(6.5)\\\\ = 0.67`

`\sf x = tan^((-1)) \ 0.67`

x = 33.8°