Question

L is the altitude of ∆JHL. Solve for x and y. ​

Answer 1

x = 18° and y = 3 units

Explanation:

The triangle Δ JHL is a right triangle with HL as the altitude.

Then ∠ HLJ = 90°.

Hence, ∠ HLI = 90° {Since JLI is a straight line}

So, Δ HLI is also a right triangle and LH is the altitude.

So, ∠ HLI = 5x = 90°

⇒ x = 18° (Answer)

Now, from Δ HLI,

HI² = HL² + LI² {Applying Pythagoras Theorem}

⇒ LI² = HI² - HL² = 5² - 4²

⇒ y² = 9

⇒ y = 3 units (Answer)