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A 20 foot ladder is placed against a wall at a 75 degree angle with the ground. The wall is perpendicular to the ground.

PART A: How high on the wall, in feet, will the ladder reach? Round your answer to the nearest tenth. Show your work.

PART B: What is the distance, in feet, from the wall to the base of the ladder? Show your work.

Answer :

Hrishiigo

Answer:

Part A)

Height = 19.3 feet

Part B)

Distance = 5.2 feet

Step-by-step explanation:

Part A)

Let ladder reaches upto the h height of the wall.

[tex] \therefore \sin \theta =\frac{h}{length\: of\: the \:ladder} [/tex]

[tex] \therefore \sin 75\degree =\frac{h}{20} [/tex]

[tex] \therefore 0.9659258263 =\frac{h}{20} [/tex]

[tex] \therefore 0.9659258263\times 20 = h [/tex]

[tex] \therefore 19.3185165 \: ft= h [/tex]

[tex] \therefore h = 19.3 \: ft= h [/tex]

Part B)

Let the distance from the wall to the base of the ladder be x feet.

[tex] \therefore \cos \theta =\frac{x}{length\: of\: the \:ladder} [/tex]

[tex] \therefore \cos 75\degree =\frac{x}{20} [/tex]

[tex] \therefore 0.2588190451 =\frac{x}{20} [/tex]

[tex] \therefore 0.2588190451\times 20 = x [/tex]

[tex] \therefore 5.1763809 \: ft= x [/tex]

[tex] \therefore x = 5.2 \: ft [/tex]

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