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cricket20 [7]
3 years ago
7

Please do both! Will mark brainliest

Mathematics
1 answer:
NikAS [45]3 years ago
6 0

Answer:

1. x = 19.9  2. x = 8.1

Step-by-step explanation:

1. Cos(x) = Adjacent/Hypotenuse  We identify that the angle of 17 degrees is next to the adjacent side of 19 and the hypotenuse is the longest side of the triangle.

Cos(17) = 19/x   We substitue in the values then rearrange to give us x.

xCos(17) = 19  We multiply both sides by x.

x = 19/Cos(17)  We divide by Cos(17).

x = 19.86814337  We put it into the calculator.

x = 19.9  Rounding to the nearest tenth is the same as rounding to 1 decimal place.

2. Tan(x) = Opposite/Adjacent  We identify that the angle of 51 degrees is opposite 10 and next to the adjacent side of x.

Tan(51) = 10/x  We substitute in the values then rearrange to give us x.

xTan(51) = 10  We multiply both sides by x.

x = 10/Tan(51)  We divide by Tan(51).

x = 8.097840332 We put it into the calculator.

x = 8.1  Rounding to the nearest tenth is the same as rounding to 1 decimal place.

Hope that helps you.

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Can you write a real world problem that uses Pythagorean theorem ?
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1) Road Trip: Let’s say two friends are meeting at a playground. Mary is already at the park but her friend Bob needs to get there taking the shortest path possible. Bob has two way he can go - he can follow the roads getting to the park - first heading south 3 miles, then heading west four miles. The total distance covered following the roads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to the park. If we apply Pythagoras's theorem to calculate the distance you will get:

(3)<span>2 </span>+ (4)2 =

9 + 16 = C2

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Walking through the field will be 2 miles shorter than walking along the roads. .

2) Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of Pythagoras' theorem to complete their work. The painter needs to determine how tall a ladder needs to be in order to safely place the base away from the wall so it won't tip over. In this case the ladder itself will be the hypotenuse. Take for example a painter who has to paint a wall which is about 3 m high. The painter has to put the base of the ladder 2 m away from the wall to ensure it won't tip. What will be the length of the ladder required by the painter to complete his work? You can calculate it using Pythagoras' theorem:

(5)<span>2 </span>+ (2)2 =

25 + 4 = C2

√100 = C

5.3 m. = C

Thus, the painter will need a ladder about 5 meters high.

3) Buying a Suitcase: Mr. Harry wants to purchase a suitcase. The shopkeeper tells Mr. Harry that he has a 30 inch of suitcase available at present and the height of the suitcase is 18 inches. Calculate the actual length of the suitcase for Mr. Harry using Pythagoras' theorem. It is calculated this way:

(18)<span>2 </span>+ (b)2 = (30)2

324 + b2 = 900

B2 = 900 – 324

b= √576

= 24 inches

6 0
3 years ago
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