Right Triangle Trigonometry — Drills
Right Triangle Trigonometry has 8 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 10 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
- Reciprocal — The flip of a fraction. The reciprocal of 35 is 53.
- Base — The number being multiplied. In 53 the base is 5.
- Hypotenuse — The side opposite the right angle — always the longest.
- Simplest radical form — No perfect square factors left under the root.
- Adjacent — The side next to that angle which is not the hypotenuse.
- Sine — sin θ = oppositehypotenuse.
- Tangent — tan θ = oppositeadjacent.
- Angle of elevation — The angle up from horizontal to a line of sight.
- Height — The perpendicular distance from the base to the opposite corner.
Ratio
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which ratio is adjacenthypotenuse?
Worked answer
cosine
cos θ = adjacenthypotenuse
Problem 2
Which ratio is oppositeadjacent?
Worked answer
tangent
tan θ = oppositeadjacent
Identifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which side of a right triangle is across the triangle from the angle you are using?
Worked answer
opposite
The opposite is across the triangle from the angle you are using.
Problem 2
Which side of a right triangle is next to the angle but not the hypotenuse?
Worked answer
adjacent
The adjacent is next to the angle but not the hypotenuse.
Side
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A right triangle has hypotenuse 16 and an angle of 65°. Find the opposite side, to one decimal place.
Worked answer
14.5
sin 65° = x16
x = 16 × 0.9063
≈ 14.5
Problem 2
A right triangle has hypotenuse 13 and an angle of 25°. Find the adjacent side, to one decimal place.
Worked answer
11.8
cos 25° = x13
x = 13 × 0.9063
≈ 11.8
Angle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A right triangle has legs 9 (opposite) and 11 (adjacent). Find the angle to one decimal place.
Worked answer
39.3
tan θ = 911 = 0.8182
θ = tan-1(0.8182) ≈ 39.3°
Problem 2
A right triangle has legs 12 (opposite) and 9 (adjacent). Find the angle to one decimal place.
Worked answer
53.1
tan θ = 129 = 1.3333
θ = tan-1(1.3333) ≈ 53.1°
Depression
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
From a cliff 71 m high, the angle of depression to a boat is 25°. Find the distance to the base, to one decimal place.
Worked answer
152.3
tan 25° = 71d
d = 710.4663
≈ 152.3 m
Problem 2
From a cliff 24 m high, the angle of depression to a boat is 25°. Find the distance to the base, to one decimal place.
Worked answer
51.5
tan 25° = 24d
d = 240.4663
≈ 51.5 m
Inverses
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What does sin-1(x) mean?
- sin(x) doubled
- the angle whose sine is that value
- 1sin x
- half of sin x
Worked answer
the angle whose sine is that value
It undoes the sine function.
sin-1(0.5) = 30°, not 1sin 0.5.
Special cases
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
In a 30-60-90 triangle the short leg is 11. Find the hypotenuse.
Worked answer
22
The hypotenuse is twice the short leg.
= 22
Problem 2
In a 30-60-90 triangle the short leg is 3. Find the hypotenuse.
Worked answer
6
The hypotenuse is twice the short leg.
= 6
Two-step
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
From a point 53 m from a tower, the angle of elevation to the top is 45°. Find the height to the nearest metre.
Worked answer
53
tan 45° = h53
h = 53 × 1.0000 ≈ 53 m
Problem 2
From a point 14 m from a tower, the angle of elevation to the top is 40°. Find the height to the nearest metre.
Worked answer
12
tan 40° = h14
h = 14 × 0.8391 ≈ 12 m