Grade 10 · Math · Geometry

10th grade Exact sine, cosine and tangent of 30°, 45° and 60°, and the reciprocal ratios worksheet

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Exact sine, cosine and tangent of 30°, 45° and 60°, and the reciprocal ratios

Grade 10 Math Worksheet

NameDate

Circle the best answer.

1.
Ari's kite string is 20 m long and makes a 60° angle with level ground. How high is the kite above the ground?
- 10 m
- 10√2 m
- 20√3/3 m
- 10√3 m
2.
Esme stands 15 m from the base of a climbing tower on level ground. The angle of elevation to the top is 60°. How tall is the tower above eye level?
- 15√3 m
- 15√3/2 m
- 15√2 m
- 5√3 m
3.
Jun works out tan 60° ÷ sin 60° exactly. What is the value?
- √3/2
- 2
- 3/2
- 1/2
4.
Kira multiplies cos 30° by tan 30° exactly. What is the product?
- 1/2
- √3/2
- 3/2
- 2
5.
Luz adds sin 60° and cos 30° exactly. What is the sum?
- 3/4
- (1 + √3)/2
- √3/2
- √3
6.
On Milo's sheet, an acute angle θ has sec θ = 2√3/3. What is cot(90° − θ)?
- √3/3
- √3
- 1
- 2√3/3
7.
On Noah's sheet, an acute angle θ has csc θ = √2. What is sin(90° − θ)?
- √3/2
- 1
- √2
- √2/2
8.
Pia's ramp makes an angle θ with the ground where cot θ = √3. The side opposite θ is 7 cm. How long is the hypotenuse?
- 7√3 cm
- 7√2 cm
- 14√3/3 cm
- 14 cm
9.
Ren's coaster is a regular hexagon with 8-cm sides. How far is it across, from the middle of one side to the middle of the opposite side?
- 8√3 cm
- 4√3 cm
- 8√2 cm
- 16 cm
10.
Tala's rectangular card has a long side of 12 cm. Its diagonal makes a 30° angle with that side. How long is the diagonal?
- 6√3 cm
- 8√3 cm
- 24 cm
- 12√3 cm

10th grade Exact sine, cosine and tangent of 30°, 45° and 60°, and the reciprocal ratios worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Exact sine, cosine and tangent of 30°, 45° and 60°, and the reciprocal ratios. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can read the exact sin, cos and tan of 30°, 45° and 60° off the special triangles and use them in a story.
I can name csc, sec and cot as flipped ratios, find them from a right triangle, and find the ratio of a complement.
I can combine exact values, test a claim with them, and use two angles of elevation to find a height.

Standard: G-SRT.C.6, G-SRT.C.7, G-SRT.C.8 (partial: special-angle values; csc, sec and cot)

Words to know

cosecant (csc): 1 ÷ sin: hypotenuse over opposite

secant (sec): 1 ÷ cos: hypotenuse over adjacent

cotangent (cot): 1 ÷ tan: adjacent over opposite

exact value: A value with roots, like √3/2, not a decimal

special triangle: A 45°-45°-90° or 30°-60°-90° right triangle

Common mistakes

Your child gave a ratio or its flip the wrong way round. csc, sec and cot are hypotenuse over opposite, hypotenuse over adjacent, and adjacent over opposite.

Your child flipped or used the wrong partner ratio. csc goes with sin, sec with cos, cot with tan.

Your child used a different trig ratio than the one the side pair needs. Name the sides you know, then choose sine, cosine or tangent.

Questions parents ask

What is the most common mistake with exact sine, cosine and tangent of 30°, 45° and 60°, and the reciprocal ratios?

Your child gave a ratio or its flip the wrong way round. csc, sec and cot are hypotenuse over opposite, hypotenuse over adjacent, and adjacent over opposite.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

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