A traveller approaches a mountain on highway. He measure the angle of elevation to the peak at each milestone , At 2 consecutive milestone the angle measured are 4° and 8°. What is the height of the peak if the distance between consecutive milestone is 1 mile. ( tan4° = 0.0699, tan8° =0.1405)
Answers
Answer:
height of the peak = 0.1391 miles if Distance between ang 4º and 8º is 1 Mile
Step-by-step explanation:
Let say Mountain Height = M Miles
and Initial Distance of traveler from base of mountain = B Miles
Tan 4° = M/B
=> M = 0.0699B
Distance of traveler from base of mountain after 1 mile = B - 1 Miles
=> Tan 8° = M/(B-1)
=> M = (B - 1) 0.1405
Equating both
0.0699B = (B - 1) 0.1405
=> 0.1405 = 0.0706B
=> B = 1.99
M = 0.0699B
=> M = 0.0699 * 1.99
=> M = 0.1391 miles
height of the peak = 0.1391 miles
here is the correct answer please mark me brainliest and give thanks
Answer:
tan 8° = DC/BC
0.1405 = y /x
y = 0.1405 x -----> Equation 1
tan 4° = y/x + 1
0.0699 (1 + x) = y ------> Equation 2
Equation 1 = Equation 2
0.1405 x = 0.0699 + 0.0699 x
0.1405 x = 0.0699 x = 0.0699
0.0706 x = 0.0699
X = 0.99
DC = y = 0.1405 x
y = 0.1405 (0.99)
y = 0.14 mile.
∴ y = 0.14 mile.
Step-by-step explanation:
@Genius