Answer:
The third side is increasing at an approximate rate of about 0.444 meters per minute.
Step-by-step explanation:
We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.
Let the angle between the two given sides be θ and let the third side be <em>c</em>.
Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.
First, convert the degrees into radians:
Hence, dθ/dt = π/90.
From the Law of Cosines:
Since <em>a</em> = 13 and <em>b</em> = 19:
Simplify:
Take the derivative of both sides with respect to <em>t: </em>
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Implicitly differentiate:
We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find <em>c: </em>
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Substitute:
Solve for dc/dt:
Evaluate. Hence:
The third side is increasing at an approximate rate of about 0.444 meters per minute.
The variable for x is twenty eight
Step-by-step explanation:
For a
Let the another angle be x then
x + 51° = 90° {being complementary angles }
x = 90° - 51°
x = 39°
For b
Let the another angle be x then
x + 113° = 180° {being supplementary angles }
x = 180° - 113°
x = 67°