Question

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6. A ladder is leaning against a building at an angle of 78 degrees with the ground. The foot of the ladder is 5 feet from the building. How high is the ladder?

7. A sledding hill is 300 yards long with a vertical drop of 27.6 yards. Find the angle of elevation between the hill and the ground at the bottom.

Answer 1

7.
`\displaystyle 5\degree`

6.
`\displaystyle 23,5\:yd.`

Step-by-step explanations:

7. When drawn out, you will notise you must use the inverce cotangent trigonometric ratio:

`\displaystyle ? = cot^(-1)\:(300)/(27,6); 5,2564149414...\degree \\ \\ \boxed{5\degree \approx\:?} \\ \\ \\ OR \\ \\ \\ ? = tan^(-1)\:(27,6)/(300); 5,2564149414...\degree \\ \\ \boxed{5\degree \approx\:?}`

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6. When drawn out, you will notise you must use the cotangent trigonometric ratio:

`\displaystyle ? = (5)/(cot\:78); 23,523150547... \\ \\ \boxed{23,5 \approx\:?} \\ \\ \\ OR \\ \\ \\ ? = 5tan\:78; 23,523150547... \\ \\ \boxed{23,5 \approx\:?}`

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Extended information on trigonometric ratios

`\displaystyle (OPPOCITE)/(HYPOTENUSE) = sin\:\theta \\ (ADJACENT)/(HYPOTENUSE) = cos\:\theta \\ (OPPOCITE)/(ADJACENT) = tan\:\theta \\ (HYPOTENUSE)/(ADJACENT) = sec\:\theta \\ (HYPOTENUSE)/(OPPOCITE) = csc\:\theta \\ (ADJACENT)/(OPPOCITE) = cot\:\theta`

Answer 2

Answers:

• 6. Approximately 23.52 feet
• 7. Approximately 5.28 degrees

The diagrams are below.

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Step-by-step explanation:

Problem 6

Refer to figure 1 shown below.

tan(angle) = opposite/adjacent

tan(78) = x/5

x = 5*tan(78)

x = 23.5231505473922

x = 23.52

Round this value however your teacher instructs. Make sure your calculator is in degree mode.

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Problem 7

Refer to figure 2 shown below.

sin(angle) = opposite/hypotenuse

sin(theta) = 27.6/300

theta = arcsin(27.6/300)

theta = 5.2786761033211

theta = 5.28 degrees

The notation arcsin or arcsine is the same as inverse sine. On many calculators this is shown as the button
`\sin^(-1)`