Answer:
Step-by-step explanation:
Given
Two sides of triangle of sides 5 ft and 7 ft
and angle between them is increasing at a rate of 0.9 radians per second
let
is the angle between them thus
Area of triangle when two sides and angle between them is given


Differentiate w.r.t time

at 


Answer:
32√5
Step-by-step explanation:
We have the right triangles PQA and PQB as well as the given right triangle QAB.
cot(PAQ) = 2/5 = QA/PQ
cot(PBQ) = 3/5 = QB/PQ
cot(PAQ) / cot(PBQ) = (2/5) / (3/5) = 2/3
cot(PAQ) / cot(PBQ) = (QA/PQ) / (QB/PQ) = QA / QB
QA / QB = 2/3
QA = (2/3) QB
QB = (3/2) QA
By the Pythagorean Theorem we have:
(QA)² + 32² = (QB)²
(QA)² + 32² = (3/2 QA)²
(QA)² + 1024 = (9/4) (QA)²
(5/4) (QA)² = 1024
(QA)² = (4/5)1024 = 4096/5
QA = 64/√5
Solve for PQ.
cot(PAQ) = QA/PQ
PQ = QA / cot(PAQ)
PQ = (64/√5) / (2/5) = 32√5
The height of the tower is 32√5.
Answer:
Option A 90,68


Step-by-step explanation:
see the attached figure to better understand the problem
The figure shows a kite
we know that
A kite properties include
1) two pairs of consecutive, congruent sides
2) congruent non-vertex angles
3) perpendicular diagonals
Find the measure of angle 1
we have that
----> by the diagonals are perpendicular
Find the measure of angle 2
we know that
triangle AEB is congruent with triangle CEB
so

In the right triangle EAB
----> by complementary angles in a right triangle
so

therefore

Answer:
10.15
Step-by-step explanation:
Subtract:
10.15 - 10.1 = 0.05
10.15 is greater than 10.1 by 0.05
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