MBF3C - Weebly
MBF3C Find Side Lengths with Primary Trig Ratios
In a right triangle, if you know an angle measure and a side length, you can use the trigonometric ratios to find the other side lengths:
sin [pic]A = [pic]
cos [pic]A = [pic]
tan [pic]A = [pic]
Example 1: Find the length of the unknown side.
1. Sketch the problem and label the sides/angles.
2. State the appropriate trig ratio. You have [pic]A and the hypotenuse. Since ? is the side opposite to [pic]A, you will need to use the sine trigonometric ratio which is:
sin [pic]A = [pic]
3. Solve the problem. Replace [pic]A with 25°, opposite side with ?, and hypotenuse with 12. So you get,
sin 25° = [pic]
12 * sin 25° = [pic] * 12
5.07141 = ?
4. Answer in a Sentence to show that you know what the numbers mean.
“The length of the unknown side is approximately 5.1 cm."
Practice Questions
1. Based on the following diagram use the values given to find the missing/indicated side:
a) [pic]A = 55°, c = 25 m ( find a
b) [pic]A = 65°, c = 32 cm ( find b
c) [pic]B = 15°, c = 42 m ( find b
d) [pic]B = 35°, c = 55 cm ( find a
1. Based on the following diagram use the values given to find the missing/indicated side:
a) [pic]A = 75°, b = 52 m ( find a
b) [pic]A = 64°, a = 23 cm ( find b
c) [pic]B = 18°, a = 24 m ( find b
d) [pic]B = 31°, b = 58 cm ( find a
2. Given the following diagram solve for the lengths of the missing sides.
3. Given the following diagram solve for the lengths of the missing sides.
Solutions:
(Note: answers should be within a decimal place depending on accuracy of numbers used.)
1. (a) a = 20.5m (b) b = 13.5cm (c) b = 10.9m (d) a = 45.1cm
2. (a) a = 194.1m (b) b = 11.2cm (c) b = 7.8m (d) a = 96.5cm
3. b = 116.6m c = 275.8m
4. a = 58.3cm c = 137.9cm
-----------------------
adjacent side to [pic]A
opposite side to [pic]A
hypotenuse
(Always opposite the right angle)
A
B
C
? = opposite
25°
12 cm = hypotenuse
A
B
C
A
B
C
b
c
a
A
C
B
b
c
a
C
A
B
25°
250 m
C
A
B
65°
125 cm
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