Please help me with number ten and twelve

Mathematics

1 answer:

jasenka [17]2 years ago

5 0

Answer: $93,\ 34^{\circ}$

Step-by-step explanation:

Given

For figure (i) both triangles are congruent

$\therefore 8x-27=4x+33\\\Rightarrow 8x-4x=33+27\\\Rightarrow 4x=60\\\Rightarrow x=15$

$\Rightarrow PQ=8x-27\\\Rightarrow PQ=93$

For figure (ii)

Two triangles WXZ and WZY are congruent

$\therefore 9x-28=5x-8\\\Rightarrow 4x=20\\\Rightarrow x=5^{\circ}\\\Rightarrow \angle YWX=2(9x-28)\\\Rightarrow \angle YWX=2(17)\\\Rightarrow \angle YWX=34^{\circ}$

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Two planes A and B start from the same place and move in different directions making an angle of 50° between them the speed of p

Alika [10]

Answer:

The distance between them is 230.65 miles

Step-by-step explanation:

Here we use the Cosine formula

$a^2 = b^2 + c^2 - 2bc\ cos\ A\\\\a^2 = 200^2 + 300^2 - 2\times 200\times 300cos50^{\circ}\\\\= 40,000 + 90,000 - 120,000cos50^{\circ}\\\\= 130,000 - 120,000 \times 0.64\\\\= 130,000 - 76,800\\\\a^2= 53,200\\\\a = \sqrt{53,200} \\\\= 230.65\ miles\ per\ hour$