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Yuki888 [10]
3 years ago
11

The angles in a triangle are in the ratio 1:2:3. Show that this triangle is a right-angled triangle. The hypotenuse of the trian

gle is 19 cm long. Calculate the length of the shortest side in the triangle

Mathematics
1 answer:
natita [175]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

(a)

Sum the parts of the ratio , 1 + 2 + 3 = 6 parts

Divide sum of angles in a triangle by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

Since there is an angle of 90° then the triangle is right.

(b)

The shortest side is the side opposite the smallest angle of 30°

Using the sine ratio and the exact value

sin30° = \frac{1}{2} , then

sin30° = \frac{opp}{hyp} = \frac{opp}{19} = \frac{1}{2} ( cross- multiply )

2 opp = 19 ( divide both sides by 2 )

opp = 9,5

Shortest side in the triangle is 9.5 cm

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Answer:

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\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)

Find the reduced row-echelon form of the augmented matrix for the system of equations:

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)\sim \left(\begin{array}{ccccc}1&-2&3&|&-2\\0&-14&16&|&36\\0&-6&0&|&36\end{array}\right)\sim \left(\begin{array}{ccccc}1&3&-2&|&-2\\0&16&-14&|&36\\0&0&-6&|&36\end{array}\right)

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Substitute y = -6 and z = -3 into the first equation:

x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5

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