Question

In a triangle ABC, the angle at B is 62°, the angle at C is 75°. AX is perpendicular to BC and the length AX = 5 m. Calculate BX and BC.

Answer 1

Using trigonometry and the given angles, BX can be calculated as 5.36 m by tangents and BC as the hypotenuse is 7.33 m by sines, both rounded to two decimal places.

Step-by-step explanation:

To solve for BX and BC in triangle ABC with angles at B and C being 62° and 75° respectively, and given that AX is perpendicular to BC and AX = 5 m, we can use trigonometry. Since we know the angles and the length of the perpendicular from A to BC, we can find BX and BC using the tangent function. The angle at A would be 180° - 62° - 75° = 43°.

The length BX can be found using the tangent of angle A:

tangent(angle A) = opposite/adjacent = AX/BX

BX = AX / tangent(angle A)

BX = 5 m / tangent(43°) = 5 m / 0.9325 = 5.36 m (rounded to two decimal places)

BC is the hypotenuse of the right-angled triangle ABX, so we can find it using the Pythagorean theorem or using the sine function:

BC = AX / sine(angle A)

BC = 5 m / sine(43°) = 5 m / 0.6820 = 7.33 m (rounded to two decimal places)