A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground. (a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°

Will the ladder be safe the way it is positioned?

(a) 64°

(b) Yes, the ladder will be safe the ingredients will be used.

Step-by-step explanation:

(a) Trigonometric function of Sine is the appropriate formula to use to solve this question. The formula is given as:

sin θ = Opposite/Hypotenuse

θ = Angle formed with the ground = ?

Opposite = 27 ft

Hypotenuse = 30 ft

Hence,

sin θ = 27 /30

θ = arc sin (27/30)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

64° is less than 70=

64° < 70°

Hence, the ladder will be safe the way it is positioned.

b. astronomers