Answer:
value of a = 6.93 m
hence , (b.)
Step-by-step explanation:
the given triangle is a right angled triangle, so
by using trigonometry.
=》
![\tan(a) = \tan(30) = \frac{1}{ \sqrt{3} }](https://tex.z-dn.net/?f=%20%5Ctan%28a%29%20%20%20%3D%20%5Ctan%2830%29%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
and we know,
=》
![\tan(a) = \frac{a}{b}](https://tex.z-dn.net/?f=%20%5Ctan%28a%29%20%20%3D%20%20%5Cfrac%7Ba%7D%7Bb%7D%20)
so, by above values of tan ( a ) we get,
=》
![\frac{a}{b} = \frac{1}{ \sqrt{3} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bb%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
=》
![\frac{a}{12} = \frac{1}{ \sqrt{3} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7B12%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
=》
![a = \frac{12}{ \sqrt{3} }](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B12%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
=》
![a = 4 \sqrt{3}](https://tex.z-dn.net/?f=a%20%3D%204%20%5Csqrt%7B3%7D%20)
=
=》
![a = 6.93](https://tex.z-dn.net/?f=a%20%3D%206.93)
hence, a = 6.93 m
Answer:
same
Step-by-step explanation:
same solution means same slope
Answer:
Option A) Circle.
Step-by-step explanation:
We are given the equation:
![(x - 3)^2 + (y - 12)^2 = 25](https://tex.z-dn.net/?f=%28x%20-%203%29%5E2%20%2B%20%28y%20-%2012%29%5E2%20%3D%2025)
A general equation of the circle is of the form:
![(x-h)^2 + (y-k)^2 = r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%20%2B%20%28y-k%29%5E2%20%3D%20r%5E2)
where (h,k) is the center of the circle and r is the radius of circle.
Comparing the two equations, we get,
![(h,k) = (3,12)\\r = \sqrt{25} = 5](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%283%2C12%29%5C%5Cr%20%3D%20%5Csqrt%7B25%7D%20%3D%205)
Thus, the given equation is equation of a circle centered at (3,12) and of radius 5 units.
The given lengths cannot form a triangle. They do not meet the requirements of the triangle inequality.
17 + 25 < 43
The triangle inequality requires each side be shorter than the sum of the other two.
Answer:
13.9 in
Step-by-step explanation:
Use the Pythagorean Theorem to answer this. Folding the paper along its diagonal produces two triangles; each one has shorter side 8.5 in and longer side 11 in. According to the Pyth. Thm., (8.5)^2 + 11^2 = 193.25, which results in the diagonal length √193.25, or approx. 13.9 in.