Solve the right triangle shown in the figure. Around lengths to two decimal places and express angles to the nearest tenth of a degree.

The sides and the angles as follows:

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

a ≈ 65.37

b ≈ 46.64

c = 80

The triangle is a right angle triangle. Using trigonometric ratios, let's find a.

sin 54.8 = opposite / hypotenuse

sin 54.8 = a / 80

a = 80 sin 54.8

a = 65.3715918668

a ≈ 65.37

let's use Pythagoras theorem to find b.

c² = a² + b²

b² = c² - a²

b² =  80² - 65²

b² = 6400 - 4225

b² = 2175

b = √2175

b = 46.6368952654

b ≈ 46.64

let's find ∠B

∠A +  ∠B +  ∠C = 180°

∠B = 180 - 54.8 - 90

∠B = 35.2°

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

The sides are as follows:

a ≈ 65.37

b ≈ 46.64

c = 80

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a = 65.37

b = 46.11

B = 35.2

Step-by-step explanation:

sin 54.8 = a / 80

a = 80 sin 54.8 = 65.3715 = 65.4

b=

b=46.1147 = 46.11

B = 180 - 90 - 54.8 = 35.2

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204