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galaxychild101
17.07.2019 •
Mathematics
Describe the possible side lengths of the 3rd side of the triangle given the lengths of the 2 other sides? 9 inches, 8 inches explain! you. : )
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Ответ:
Using a theoram about triangles ,
Given a triangle ∆ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side ,
Also , the length of third side always greater than absolute difference of the other two sides ,
Let the third side be x ,
So , x < 9 + 8 and x > 9 - 8
x < 17 and x > 1
Hence , x ∈ [ 2 , 17 ] inch.
Above case is true for any triangle , be it scalene , Isosceles , Right-angled ...
As , for Isosceles , the third side can be 8 or 9 inches ,
For scalene , all values in the above range satusfies ,
For right angled triangle , we have 2 cases ,
Case 1 : Third side is the hypotenuse
Then , x = √(9²+8²) = √145 = 12.0415 inch.
Case 2 : Third side is not the hypotenuse
Then , x = √(9²-8²) = √17 = 4.1231 inch.
Hope it helps you ! :)
Ответ:
Remember to use the a² + b² = c² formula.
let the hypotenuse side be "x".
9² + 8² = x²
Simplify
81 + 64 = x²
Add
x² = 145
Root both sides
√x² = √145
Answer
x = 12.04159 (rounded)
let one of the sides (not hypotenuse) be x
9²- 8² = x²
Simplify
81 - 64 = x²
Subtract
x² = 17
Root both sides to isolate the x
√x² = √17
Answer
x = 4.12310 (rounded)
hope this helps
Ответ:
1. a = 32.96 m∠B = 21° b = 12.74
2. x = 24.99
Step-by-step explanation:
1. Use the law of sines:
a/sin 112 = 26/sin 47
a = 26 sin 112/sin 47
a = 32.96
m∠B = 180 - 47 - 112 = 21°
b/sin 21 = 26/sin 47
b = 26 sin 21/sin 47
b = 12.74
2. Use the law of cosines
= 289 + 121 - 374 cos 125
= 624.5175....
x =![\sqrt{624.5175...}](/tpl/images/1359/2713/d8636.png)
= 24.99