From an observation tower that overlooks a small lake, the angles of depression of point A, on one side of the lake, and point B, on the opposite side of the lake are, 7degrees and 13degrees, respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1km. Determine the height of the tower.
I made a side view diagram, with A and B the points on the lake, obviously A farther away from the tower. I labeled my tower DC , C as the base of the tower.
In Triangle ABD, angle A = 7°, angle ABD = 167° , angle ADB = 6° , and AB = 1 km
by the sine law:
BD/sin7 = 1/sin6
BD = sin7/sin6 = 1.16589... (keep number in calculator's memory)
Now in the right-angled triangle, BCD
DC/BD = sin13
DC = 1.16589..(sin13) = .26226 km
or appr 226 m
A children's play area is triangular the sides of the play area measure 100m 250m and 275 respectively. Calculate the area of the play area
Triangle is A-B 275m, B-C 250m, A-C 100m
First use a^2-b^2-c^2/-2bc=CosA
Then this to calculate area A=(1/2) bc SinA
Answer should be A=12,479m^2
Good Luck
To determine the height of the tower, we can use trigonometry and create a right triangle.
Let's label the height of the tower as 'h', the distance from point A to the tower as 'd1', and the distance from point B to the tower as 'd2'.
From the information given, we know that the angles of depression are 7 degrees and 13 degrees. The angles of depression are the angles formed between the line of sight from the observation tower to the points A and B and the horizontal line.
Since the angles of depression form a right triangle with the horizontal line, the angles of elevation from points A and B to the top of the tower are also 7 degrees and 13 degrees respectively. The angles of elevation are the angles formed between the line of sight from points A and B to the top of the tower and the horizontal line.
Now, let's consider the triangle formed by the tower, point A, and point B.
Since the distance from A to B is 1 km, we can conclude that d1 + d2 = 1 km.
To find the height of the tower, we need to determine the values of d1 and d2.
Using trigonometry, we can set up the following equations:
tan(7 degrees) = h / d1 (1)
tan(13 degrees) = h / d2 (2)
Now, we need to solve these two equations simultaneously to find the values of d1 and d2.
From equation (1), we can rearrange it to:
d1 = h / tan(7 degrees)
Similarly, from equation (2), we can rearrange it to:
d2 = h / tan(13 degrees)
Substituting these values into the equation d1 + d2 = 1 km, we have:
h / tan(7 degrees) + h / tan(13 degrees) = 1 km
Now, we can solve this equation to find the value of h, the height of the tower.