SSS2 Math Quiz 12.4 – Outcome tables and tree diagrams

If sin P = 3/5 and P is an acute angle of a right-angled triangle, what is the value of tan P?

Given that tan x = 5/12, what is the value of sin x + cos x?

From a point P on level ground, the angle of elevation of the top of a tree is 60 degrees. If the tree is 30 m high, how far is its base from P?

A regular hexagon has 6 sides of length 6 cm. Find the perpendicular distance between two opposite faces.

If tan x = 8/15, find the value of (sin x + cos x) / (cos x * (1 – cos x))

The length of a diagonal of a square field is 180 m. Find the length of a side in meters and the area of the field in hectares.

A student stands 25 m away from the foot of a tree and observes that the angle of elevation of the top of the tree, measured from a table 1.2 m above the ground, is 30 degrees. Calculate the height of the tree to the nearest meter.

The shadow of a post is 8 m longer when the elevation of the sun is 30 degrees than when it is 60 degrees. Calculate the height of the post.

If cos θ = 12/13 and θ is an acute angle, find the value of sin θ – tan θ

A ladder leans against a wall at an angle of 60 degrees to the ground. If the foot of the ladder is 5 m from the wall, how high up the wall does the ladder reach?

The angle of depression of a boat from the top of a cliff 80 m high is 30 degrees. How far is the boat from the foot of the cliff?

A man walks 100 m due North and then 50 m due East. Find his bearing from his starting point.

If sin A = 4/5 and cos B = 12/13, where A and B are acute angles, find the value of sin(A + B).

A circle has a radius of 10 cm. Find the length of an arc subtended by a central angle of 120 degrees.

The area of a sector of a circle with radius 5 cm is 15π cm². Find the central angle of the sector in degrees.

A rectangular garden has a length of 12 m and a width of 5 m. A path 1 m wide is built around the garden. Find the area of the path.

The volume of a cone is 36π cm³ and its height is 9 cm. Find its radius.

A pyramid has a square base of side 6 cm and a slant height of 5 cm. Find its total surface area.

Two similar cylinders have radii in the ratio 2:3. If the volume of the smaller cylinder is 40 cm³, find the volume of the larger cylinder.

In a parallelogram ABCD, AB = 10 cm, BC = 7 cm, and angle ABC = 120°. Find the area of the parallelogram.