Trigonometry Worksheet (Copy/Paste)
*Answers are below
a) Triangle ABC – 90 degree angle is B, 45 degrees in angle C, mBC = 20cm. What is the measurement of side AB?
b) Triangle RST – right angle in R, mRT = 12m and a hypotenuse (mST) of 15m. What is the value of angle S?
c) Triangle QRS – right angle in Q and angle R = 63 degrees, mRQ = 8mm. What is the length of side QS?
d) Triangle ABC – right angle in A, mAC = 14cm, mAB = 10cm. What is the length of side BC?
e) Triangle FGH – 90 degree angle is F, opposite the right angle is measurement FH = 38m. What is the measurement of FG?
f) Triangle RST – right angle in T, angle S = 31 degrees. What is the value of angle R?
g) Triangle TUV – right angle in U, hypotenuse mTV = 28m. What is the value of angle V?
h) Triangle ABC – right angle in A, mAC = 21mm, mCB = 32mm. What is the length of AB?
i) Triangle FGH – 90 degree angle is G, mFG = 6m. What is the length of the hypotenuse mFH?
j) Triangle QRS – 90 degree angle is Q, mQS = 17cm, mQR = 12cm. What is the value of angle R?
k) The two acute angles in a right triangle are A and B. Angle C is therefore the right angle. The sides opposite these angles are a, b and c respectively. If angle B = 38 degrees and b = 8cm, determine the length of the hypotenuse to the nearest cm.
l) In a right triangle, C is the right angle and A and B are its actue angles. The sides opposite these angles are a, b and c. If angle B measures 58 degrees and side a, 18cm, determine the length of side b in this triangle, to the nearest cm.
m) Given a triangle ABC, right angle in C with known dimensions of angle B = 28 degrees and side c = 138cm. Determine the legths of sides a and b in this right triangle to the nearest cm.
n) Given triangle ABC, with right angle in C, determine the measure of angle B to the nearest degree and the length of side c if b = 20m and a = 37m.
o) Given right angle triangle ABC with 90 degrees in C, determine the measure of angle A and angle B to the nearest degree is b = 147cm and a = 419cm.
p) Given triangle ABC with 90 degrees in C, determine the dimensions of the other side and of the two acute angles to the nearest cm and degree if b = 54cm and c = 108cm.
Word Problems:
q) From the top of an 23m high observation tower located on a hill 315m high, you spot a car accident on the road. If you then measure an 21 degree angle of depression between the horizon and the location of the accident, determine how far you are from the site of the accident. Give your answer to the nearest metre.
r) What would the length of the shadow cast by a 21.6m highg tree be, if at that moment the sun's angle of elevation was 48.3 degrees?
s) What would the length of the shadow bast by a 170m building be, if at that moment the sun's angle of elevation was 67 degrees?
Answers:
a) 20cm
b) 53 degrees
c) 15.7mm
d) 17.2cm
e) 35.5m
f) 59 degrees
g) 55.2 degrees
h) 24.1mm
i) 6.3m
j) 54.8 degrees
k) 13cm
l) 29cm
m) side b = 65cm; side a = 122cm
n) side c = 42m; angle B = 28 degrees
o) angle A = 71 degrees; angle B = 19 degrees
p) side a = 94cm; angle A = 60 degrees; angle B = 30 degrees
q) 929m
r) 19cm
s) 72m
*Answers are below
a) Triangle ABC – 90 degree angle is B, 45 degrees in angle C, mBC = 20cm. What is the measurement of side AB?
b) Triangle RST – right angle in R, mRT = 12m and a hypotenuse (mST) of 15m. What is the value of angle S?
c) Triangle QRS – right angle in Q and angle R = 63 degrees, mRQ = 8mm. What is the length of side QS?
d) Triangle ABC – right angle in A, mAC = 14cm, mAB = 10cm. What is the length of side BC?
e) Triangle FGH – 90 degree angle is F, opposite the right angle is measurement FH = 38m. What is the measurement of FG?
f) Triangle RST – right angle in T, angle S = 31 degrees. What is the value of angle R?
g) Triangle TUV – right angle in U, hypotenuse mTV = 28m. What is the value of angle V?
h) Triangle ABC – right angle in A, mAC = 21mm, mCB = 32mm. What is the length of AB?
i) Triangle FGH – 90 degree angle is G, mFG = 6m. What is the length of the hypotenuse mFH?
j) Triangle QRS – 90 degree angle is Q, mQS = 17cm, mQR = 12cm. What is the value of angle R?
k) The two acute angles in a right triangle are A and B. Angle C is therefore the right angle. The sides opposite these angles are a, b and c respectively. If angle B = 38 degrees and b = 8cm, determine the length of the hypotenuse to the nearest cm.
l) In a right triangle, C is the right angle and A and B are its actue angles. The sides opposite these angles are a, b and c. If angle B measures 58 degrees and side a, 18cm, determine the length of side b in this triangle, to the nearest cm.
m) Given a triangle ABC, right angle in C with known dimensions of angle B = 28 degrees and side c = 138cm. Determine the legths of sides a and b in this right triangle to the nearest cm.
n) Given triangle ABC, with right angle in C, determine the measure of angle B to the nearest degree and the length of side c if b = 20m and a = 37m.
o) Given right angle triangle ABC with 90 degrees in C, determine the measure of angle A and angle B to the nearest degree is b = 147cm and a = 419cm.
p) Given triangle ABC with 90 degrees in C, determine the dimensions of the other side and of the two acute angles to the nearest cm and degree if b = 54cm and c = 108cm.
Word Problems:
q) From the top of an 23m high observation tower located on a hill 315m high, you spot a car accident on the road. If you then measure an 21 degree angle of depression between the horizon and the location of the accident, determine how far you are from the site of the accident. Give your answer to the nearest metre.
r) What would the length of the shadow cast by a 21.6m highg tree be, if at that moment the sun's angle of elevation was 48.3 degrees?
s) What would the length of the shadow bast by a 170m building be, if at that moment the sun's angle of elevation was 67 degrees?
Answers:
a) 20cm
b) 53 degrees
c) 15.7mm
d) 17.2cm
e) 35.5m
f) 59 degrees
g) 55.2 degrees
h) 24.1mm
i) 6.3m
j) 54.8 degrees
k) 13cm
l) 29cm
m) side b = 65cm; side a = 122cm
n) side c = 42m; angle B = 28 degrees
o) angle A = 71 degrees; angle B = 19 degrees
p) side a = 94cm; angle A = 60 degrees; angle B = 30 degrees
q) 929m
r) 19cm
s) 72m