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lidiya [134]
3 years ago
10

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

Mathematics
1 answer:
sweet [91]3 years ago
8 0

Answer:

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

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Answer:

a.x=10 \textdegree

b.

m\angle L=39\textdegree\\\\m\angle M=51\textdegree\\\\m\angle K=90\textdegree

Step-by-step explanation:

a. We know that angles in a triangle add up to 180°.

-The right angle triangle in the right triangle has a measure of 90°.

We can therefore equate our angles to 180° and solve for x;

180=\perp\angle+(2x+19)+(3x+21)\\\\180=90+(2x+19)+(3x+21)\\\\90=5x+40\\\\5x=50\\\\x=10\textdegree

Hence, the angle measure is x=10°

b. Having calculated the value of x from a above as x=10°, we can substitute to find the measures of the two acute angles:

m\angle L=(2x+19)\textdegree\\\\=(2\times 10+19)\textdegree\\\\=39\textdegree\\\\m\angle M=(3x+21)\textdegree\\\\=(3\times 10+21)\textdegree\\\\=51\textdegree

Since, the m∠K is a right angle, it measures 90°

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Step-by-step explanation:

5/2

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