SLFJ SDFNEFS LF A SF IE FJS VS IKF DSFNIS DSF
1 answer:
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9514 1404 393
Answer:
3. no; does not have the correct ratio to other sides
4. (1; right), (2; obtuse), (3; right)
Step-by-step explanation:
3. There are a couple of ways you can go at this.
a) the ratio of sides of a 30°-60°-90° right triangle (half an equilateral triangle) is 1 : √3 : 2. Here, the ratio of sides is ...
(√30/2) : √15 : √30 = 1 : √2 : 2 . . . . MQ is <em>not</em> the height
b) the height is perpendicular to the base, so if MQ were the height, the sides of the triangle would satisfy the Pythagorean theorem:
LQ² +MQ² = LM²
(√30/2)² +(√15)² = (√30)²
30/4 +15 = 30
22.5 = 30 . . . . NOT TRUE
The length MQ cannot be the height of ∆LMN. (It is too short.)
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4. To see if these lengths form a right triangle, you can test them in the Pythagorean theorem relation. In the attached we have reformulated the equation so it gives a value of 0 if the triangle is a right triangle:
c² = a² +b² . . . . . Pythagorean theorem
c² -a² -b² = 0 . . . . rewritten
If the value of c² -a² -b² is not zero, then the side lengths do not form a right triangle. The attached shows this math performed by a graphing calculator. The results are ...
- right triangle
- not a right triangle — long side is too long, so the triangle is obtuse
- right triangle
_____
<em>Additional comment</em>
The attached table demonstrates an artifact of computer arithmetic. Not all numbers can be represented exactly in a computer, so a difference that is expected to be zero using exact arithmetic may be slightly different from zero when computed by a computer or calculator. Here, we see a difference of about 6×10^-14 when zero is expected. On most calculators (with 10, or 12 displayed digits), this would be displayed as 0.
The same calculation done "by hand" gives ...
(√425)² -5² -20² = 425 -25 -400 = 0 . . . Triangle 1 is a <em>right triangle</em>
Answer:
AB = 13.89
Measure of angle A = 59.74°
Measure of angle B = 30.26°
Step-by-step explanation:
The given parameters are;
∠C = 90°
AC = 7
BC = 12
Part 1
Hence, the question has the dimensions of the two adjacent sides of the right angle (angle 90°)
From Pythagoras theorem, we have;
A² = B² + C²
Where, A is the opposite side to the right angle, hence;
In the ΔABC,
AB ≡ A
Therefore;
AB² = AC² + BC² = 7² + 12² = 193
∴ AB = √193 = 13.89
Part 2
∠A is the side opposite side BC such that by trigonometric ratios
∴ ∠A = Arctan(1.714) or tan⁻¹(1.714) = 59.74°
Part 3
∠B is found from knowing that the sum of the angles in a triangle = 180°
∴ ∠A + ∠B + ∠C = 180° which gives
59.74° + 90° + ∠B = 180°
Hence, ∠B = 180° - (59.74° + 90°) = 180° - 149.74° = 30.26°.