Question

Plz help to solve fast before exam :)

Answer 1

see explanation

Explanation:

(a)

the area( A ) of a trapezium is calculated using the formula

A =
`(h)/(2)`(a + b)

where a and b are the lengths of the parallel sides and h is the perpendicular height between them

here a = 13x, b = 17x + 12 and h = 5

A =
`(5)/(2)`(13x + 17x + 12) =
`(5)/(2)`(30x + 12)

A = 5(15x + 6) = 75x + 30 cm²

(b) ΔABC is a right triangle so we can use the sine ratio to solve for y

We require to find BC using Pythagoras' identity

BC² = 5² + 12² = 25 + 144 = 169

⇒ BC =
`√(169)` = 13, hence

sin y° =
`(opposite)/(hypotenuse)` =
`(5)/(13)`

⇒ y =
`sin^(-1)`(
`(5)/(13)`) = 22.6° ( to 1 dec. place )