به انگلیسی

Angles you just know

Mathematics · Geometry · ages 15-16

Name ______________________ Date ____________

What is tan 45 degrees?
Answer: ______________
What is cos 30 degrees?
- root 3 over 2
- 1/2
- root 2 over 2
What is sin 30 degrees?
- 1/2
- 1/4
- 1
Tan 45 degrees equals 1 because the two legs of the triangle are equal.
Circle one: True False
Halving an equilateral triangle of side 12 gives a right angled triangle with hypotenuse 12. What is the leg adjacent to the 60 degree angle?
- 12
- 6
- 6 root 3
Which of these should be left in surd form rather than rounded?
- Sin 60 degrees
- Sin 30 degrees
- Tan 45 degrees
An equilateral triangle with side length 8 is cut in half down the middle. What is the length of the shortest side of each half?
Answer: ______________
Which of these values is undefined?
- tan 90 degrees
- tan 45 degrees
- sin 30 degrees
A right angled triangle has a 45 degree angle and the leg adjacent to that angle is 9 cm long. How long is the side opposite the angle, in cm?
Answer: ______________
A right angled triangle has a 45 degree angle and the leg adjacent to that angle is 7 cm long. How long is the side opposite the angle, in cm?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

1 · Tan 45 is opposite over adjacent, and the two legs of a 45-45-90 triangle are equal, so the answer is 1.
root 3 over 2 · Cos 30 is the long leg over the hypotenuse in a halved equilateral triangle, which is root 3 over 2.
1/2 · Sin 30 is one half, the first of the must-know trio.
True · Opposite over adjacent with equal legs gives exactly 1.
6 · The leg adjacent to 60 degrees is the short leg, half the original side, so 12 becomes 6.
Sin 60 degrees · Sin 60 is root 3 over 2, which never comes out neat.
4 · The cut splits one side of 8 into two equal halves of 4, and the shortest side of each half is 4.
tan 90 degrees · Tan 90 is y over x at the point (0, 1), which is 1 over 0, undefined.
9 · Tan 45 is 1, so opposite equals adjacent, which is 9 cm.
7 · Tan 45 is 1, so opposite equals adjacent, which is 7 cm.