In a triangle HIJ, i = 6.6 inches, j = 6.4 inches and Angle, H=62º. Find the length of h, to the nearest 10th of an inch.

7.6 inches

Step-by-step explanation:

We solve the above question using the Law of Cosines.

The formula is given as:

h² = i² + j² - 2ij Cos H

h = √i² + j² - 2ij Cos H

From the above question:

i = 6.6 inches

j = 6.4 inches

Length h = ?

Angle H=62º.

Hence:

h= √6.6² + 6.4² - 2 × 6.6 × 64 × Cos 62

h = √43.56 + 40.96 - 84.48 × Cos 62

h = 7.64292 inches

Approximately to the nearest tenth, Length h = 7.6 inches

1 1/5

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.