Answer:
10.76 miles
Step-by-step explanation:
<em>The following figure can be drawn from the information given.</em>
<em>We have to find the adjacent side which is between the given angle and 90 degrees.</em>
<em>Tan formula will be applied</em>
Tan (anlge) = opposite/adjacent
Opposite = 12.6
Angle = 49.5°
Adjacent = x
Tan (49.5°) = 12.6/x
x = 10.76 miles
Therefore, the fire is 10.76 miles away from the tower Pikes Peak.
!!
Answer:
c = 13.2
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# Side a is opposite to ∠A
# Side b is opposite to ∠B
# Side c is opposite to ∠C
- The sine rule is:
#
* Lets solve the problem
- In Δ ABC
∵ m∠A = 16°
∵ m∠B = 49°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 16° + 49° + m∠C = 180°
∴ 65° + m∠C = 180° ⇒ subtract 65° from both sides
∴ m∠C = 115°
- Lets use the sine rule to find c
∵ a = 4 and m∠A = 16°
∵ m∠C = 115°
∵
- By using cross multiplication
∴ c sin(16) = 4 sin(115) ⇒ divide both sides by sin(16)
∴
* c = 13.2