Question

X, Y and Z form the vertices of a triangle with area 59.7cm2. If XZ = 21.5cm and XY = 13.5cm, work out the acute angle ∠YXZ. Round to 1 DP.

Answer 1

Answer: The acute angle ∠YXZ = 24.3°.

Explanation:

If in triangle ABC, C is the angle included between sides a and b then

Area of triangle =
`\frac12a\cdot b\cdot sin C`

here, XZ = 21.5cm and XY = 13.5cm are sides that includes acute angle ∠YXZ..

Area of a triangle = 59.7cm²

then, as per given, we have

`59.7=\frac12(21.5)(13.5)\ \sin X\\\\\Rightarrow\ 59.7=145.125\ \sin X\\\\\Rightarrow\ \sin X = (59.7)/(145.125)\\\\\Rightarrow\ \sin X =0.41137\\\\\Rightarrow\ X = \sin ^(-1)(0.41137)\approx24.3^(\circ)`

Hence, the acute angle ∠YXZ = 24.3°.