Question

Please help really important for my grade :(

Answer 1

≈ 50.7 cm²

Explanation:

The area (A) of Δ XYZ is calculated as

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

A =
`(1)/(2)` × XY × YZ

Calculate YZ using the tangent ratio in the right triangle

tan40° =
`(opposite)/(adjacent)` =
`(YZ)/(XY)` =
`(x)/(11)` ( multiply both sides by 11 )

11 × tan40° = x , that is

YZ ≈ 9.23 cm

Thus

A =
`(1)/(2)` × 11 × 9.23 = 5.5 × 9.23 ≈ 50.7 cm² ( to 3 significant figures )