Answer :
The length of the missing side is A) 3.4 cm.
To find side AB in the right triangle ABC given that angle A is 17 degrees and side BC is 11 cm, we'll use the trigonometric function sine since we have an angle and its opposite side. The sine function relates the length of the opposite side to the hypotenuse.
[tex]\[ \sin(A) = \frac{opposite}{hypotenuse} \]\[ \sin(17^\circ) = \frac{AB}{11} \][/tex]
Now, we solve for AB:
[tex]\[ AB = 11 \times \sin(17^\circ) \][/tex]
Using a calculator:
[tex]\[ AB \approx 11 \times 0.29237 \]\[ AB \approx 3.21607 \][/tex]
Rounded to the nearest tenth:
AB = 3.2
So, the missing side AB is approximately 3.2 cm. Among the options provided, the closest one is 3.4 cm (option a).
Complete Question:
ABC is a right angle triangle with angle A as 17 degree, BC 11 cm. Find the missing side AB. Round to the nearest tenth.
a. 3.4
b. 36.0
c. 38.6
d. 41.2
tan(angle) = opposite/adjacent
tan(17) = 11/x
x*tan(17) = 11 .... multiply both sides by x
x = 11/tan(17) ...... divide both sides by tan(17)
x = 35.9793788 .... use your calculator
x = 36.0
