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
1 answer:
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° = , then
sin30° = =
=
( 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:
B 1
Step-by-step explanation:
Since the divisor is in the form of <em>x - c</em>, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
2| -2 1 5 0 4 1
↓ -4 -6 -2 -4 0
_________________
-2 -3 -1 -2 0 1→ -2x⁴ - 3x³ - x² -2x + [x - 2]⁻¹
You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [-2x⁵ + x⁴ + 5x³ + 4x + 1]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is, tells you whether the next step is to <em>subtract</em> or <em>add</em>, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that -2 in your quotient can be a -2x⁴, and the -3 [x³] follows right behind it, then 1 [-x²], -2[x], and finally, [1\x - 2] (remainder is 1, so set it over your denominator, which is the divisor), giving you the other factor of -2x⁴ - 3x³ - x² -2x + [x - 2]⁻¹.
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