A ladder leans up against a wall and makes a 60 degree angle with the ground. If it reaches 90 ft. up the wall, how long is the ladder? Round to the nearest tenth

The length is approximately 103.92 ft

Step-by-step explanation:

The angle the given ladder makes with the ground = 60°

The height to which the ladder reaches. h = 90 ft.

Assumption;

The angle formed between the wall and ground = 90°

The shape formed by the length, l, of the ladder the height to which the ladder reaches on the wall, h, and the ground, b, is a right triangle, with the length, l, of the ladder facing the 90° angle and the height, h, facing the 60° angle.

By sine rule, we have;

l/sin(90°) = h/sin(60°)

Therefore, the length l = sin(90°) × h/sin(60°) = 1 × 90/(sin(60°)) = 90/((√3)/2) = 2 × 90/√3 ≈ 103.92

The length, l ≈ 103.92 ft.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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step-by-step explanation: