Question

Question 5 (4 marks)

Albert, Lisa and Queenie are all standing on level ground, looking up at a plane P.
The angle of elevation from Albert to the plane is 40° and from Lisa to the plane is 70°.
Lisa is 90m away from Albert and Queenie is 170m from Lisa, as shown in the diagram.
b)
40°
90-
x
70°
-170-
Find the distance, x from Lisa to the plane, to the nearest metre.
Q
Hence find the distance, y from Queenie to the plane, to the nearest metre.
Marks
2

Answer 1

To find the distance, x, from Lisa to the plane, we can use trigonometry.

Since Lisa and Albert form a right triangle, we can use the tangent function:

tan(40°) = Opposite/Adjacent

tan(40°) = x/90

To find x, we can rearrange the equation:

x = 90 * tan(40°)

Using a calculator, we can find:

x ≈ 72.92

Rounding x to the nearest meter, we get x = 73 meters.

To find the distance, y, from Queenie to the plane, we can use the same concept. Queenie is 170 meters away from Lisa, so we have a right triangle with sides 170 and y.

Again, using the tangent function:

tan(70°) = Opposite/Adjacent

tan(70°) = y/170

Rearranging the equation, we get:

y = 170 * tan(70°)

Using a calculator, we find:

y ≈ 463.26

Rounding y to the nearest meter, we get y = 463 meters.