Triangles ABC and DEF are similar, which means corresponding sides occur in ratios with one another. Mathematically, this means
Also, corresponding angles are congruent. These are A and D, B and E, C and F.
As an example, for 21, the above equation turns into
and you can solve for and directly:
The others are solved exactly the same way. In each case, you happen to be given all the side lengths for one of the triangles, and one of the side lengths for the other triangle. So all you need to do is plug in what you know and solve for the remaining two sides.
You have to build the triangles.
They are such that:
h is the common height
x is the horizontal distance from the plane to one stone
Beta is the angle between x and the hypotenuse
Then in this triangle: tan(beta) = h / x ......(1)
1 - x is the horizontal distance from the plane to the other stone
alfa is the angle between 1 - x and h
Then, in this triangle: tan (alfa) = h / [1 -x ] ...... (2)
from (1) , x = h / tan(beta)
Substitute this value in (2)
tan(alfa) = h / { [ 1 - h / tan(beta)] } =>
{ [ 1 - h / tan(beta) ] } tan(alfa) = h
[tan(beta) - h] tan(alfa) = h*tan(beta)
tan(beta)tan(alfa) - htan(alfa) = htan(beta)
h [tan(alfa) + tan(beta) ] = tan(beta) tan (alfa)
h = tan(beta)*tan(alfa) / (t an(alfa) + tan(beta) )
Answer:
Step-by-step explanation:
Answer:
55
Step-by-step explanation:
Given in the picture that factor tree for 3025 in which the factors are
5, 5, 11, 11.
To find,
<h3>the simplest form of √3025</h3>
√3025
√(5 x 5 x 11 x 11)
√(5² x 11²)
√5²√11²
<em>As we know that square and square root on same integer cancel each other</em>
So,
(5)*(11)
55 Answer