CH is an altitude of the triangle ABC, m∠A = 60°, m∠B = 45°. Circle with the diameter CH intersects sides AC and BC at points N
and M respectively. Find the area (exact value) of the quadrilateral CMHN if AN = 1.
1 answer:
Answer:
(6+3√3)/2
Step-by-step explanation:
ΔANH is a 30°-60°-90° right triangle. The side lengths of such a triangle are in the ratio 1 : √3 : 2. This means side NH has length √3, and segment NC has length 3. The altitude CH is then 2√3, so the radius of the circle is √3.
The area of triangle CHN is ...
(1/2)(√3)(3) = (3/2)√3
The area of triangle CHM is ...
(1/2)(2√3)(√3) = 3
Then the area of quadrilateral CMHN is ...
3 + (3/2)√3 = (6+3√3)/2
You might be interested in
Answer:
2,000 miles
Step-by-step explanation:
We are given:
This can be rewritten as:
This is representative of a unit rate, as we have a in the denominator. To calculate the number of miles in
inches, simply multiply the unit rate by
:
This can rewritten as:
Therefore, there are 2,000 miles in 4 inches.
-
We can check our solution by simplifying the fraction by dividing both
and
by
to see if we achieve the unit rate:
Since this is in fact the unit rate, our solution is correct!