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Trigonometry — Question 300

Original QCE Vault practice · 4 marks

Q300 · Practice questionTechnology-activeSimple familiar4 marks

QUESTION 300 (4 marks)

A rectangular rooftop is

8

m by

6

m. A vertical

12

m mast stands at corner

B

, diagonally opposite corner

A

. The top of the mast is

T

.

Single perspective view of an 8 m by 6 m rectangular rooftop, projected from orthogonal sides in 3D. A is diagonally opposite B. A vertical 12 m mast BT and cable AT form a right triangle with dashed roof diagonal AB; theta is the angle between the cable and the roof diagonal. Right-angle marks identify the rectangular roof corner and the perpendicular mast. Not to scale.

a)

Determine the exact length of a straight cable from

A

to

T

.

[2 marks]

b)

Determine the angle the cable makes with the rooftop, to

0.1^\circ

.

[2 marks]

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