From the top of From a cliff the angle of depression of the top of a tower is 45° . The horizontal distance between the cliff and the tower is 3 under root 2 km . What is the distance between the top of the cliff and the top of the tower?
Answers
10th
Maths
Some Applications of Trigonometry
Heights and Distances
From the top of a hill, the...
MATHS
From the top of a hill, the angles of depression of two consecutive kilometer stones due east are found to be 30o and 45o. Find the height of the hill
A
1.365km
Correct Answer
B
1.5km
C
1.7km
Your Answer
D
1.1km
HARD
Share
Study later
ANSWER
Let the distance between the nearer kilometre stone and the hill be 'x' km.
So, the distance between the farther kilometre stone and the hill is '1+x' km since both are on the same side of the hill.
In triangle APB,
tan450=xh
⇒1=xh
⇒h=x
In triangle AQB,
tan300=1+xh
⇒31=1+xh
⇒1+x=3h
From equation 1,
1+h=3h⇒1=3h−h
⇒h=3
Answer:
6km
Step-by-step explanation:
Here, ∆ ABC is right triangle.
A and C are the points at the top.
angle BAC=45°
AB is the horizontal distance between them.
So, AB= 3√2 km.
We need to find the distance their tops or the length AC.
Finding the length
We can use cos(45°) to find AC.
cos(A) = AB/AC
cos(45°)=3√2/x
1/√2 = 3√2/x
x=6
