Question

Plsss solve this i need help,explain thoroughlyy

Answer 1

x ≈ 41.2°

Explanation:

the first step is to find AC

Then we can use the tangent ratio to find x

the area ( A ) of a triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the perpendicular height )

given area of Δ ABC = 42 cm² , then

`(1)/(2)` × BC × AC = 42 , that is

`(1)/(2)` × 6 × AC = 42

3 AC = 42 ( divide both sides by 3 )

AC = 14 cm

----------------------------------------------------

given BD = 22 cm , and BC = 6 cm , then

BC + CD = BD ( substitute values )

6 + CD = 22 ( subtract 6 from both sides )

CD = 16 cm

using the tangent ratio in right triangle ACD

tan x =
`(opposite)/(adjacent)` =
`(AC)/(CD)` =
`(14)/(16)` , then

x =
`tan^(-1)` (
`(14)/(16)` ) ≈ 41.2° ( to the nearest tenth )