Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = , then letting the altitude be h
tan60° = =
=
( multiply both sides by h )
11 = h ×
( divide both sides by
)
11 = h
using the sine ratio in the triangle on the left and the exact value
sin45° = , then
sin45° = =
=
=
( cross- multiply )
× x = 22
( divide both sides by
)
x = 22
Answer:
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
Step-by-step explanation:
From Geometry we understand that area of triangle is determined by the following expression:
(Eq. 1)
Where:
- Area of the triangle, measured in square centimeters.
- Base of the triangle, measured in centimeters.
- Height of the triangle, measured in centimeters.
By Differential Calculus we deduce an expression for the rate of change of the area in time:
(Eq. 2)
Where:
- Rate of change of area in time, measured in square centimeters per minute.
- Rate of change of base in time, measured in centimeters per minute.
- Rate of change of height in time, measured in centimeters per minute.
Now we clear the rate of change of base in time within (Eq, 2):
(Eq. 3)
The base of the triangle can be found clearing respective variable within (Eq. 1):
If we know that ,
,
and
, the rate of change of the base of the triangle in time is:
The base of the triangle decreases at a rate of 2.262 centimeters per minute.