9514 1404 393
Answer:
10°, 80°
Step-by-step explanation:
<em><u>Setup</u></em>
Let x and y represent the measures of the two acute angles in the right triangle.
From your knowledge of right triangles, you know the two acute angles are complementary:
x + y = 90
The problem statement gives you another relation:
x = 2(y + 30) . . . . twice the sum ...
__
<em><u>Solution</u></em>
The second equation gives you an expression for x that can be substituted into the first equation.
(2(y +30)) + y = 90
3y +60 = 90 . . . . . . . . collect terms
3y = 30 . . . . . . . . . subtract 60
y = 10 . . . . . . . . divide by 3
x = 2(y +30) = 2(40) = 80
The two angles are 10° and 80°.
Find tan (22.5)
Answer: #-1 + sqrt2#
Explanation:
Call tan (22.5) = tan t --> tan 2t = tan 45 = 1
Use trig identity: # tan 2t = (2tan t)/(1 - tan^2 t)# (1)
#tan 2t = 1 = (2tan t)/(1 - tan^2 t)# -->
--> #tan^2 t + 2(tan t) - 1 = 0#
Solve this quadratic equation for tan t.
#D = d^2 = b^2 - 4ac = 4 + 4 = 8# --> #d = +- 2sqrt2#
There are 2 real roots:
tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2
Answer:
#tan t = tan (22.5) = - 1 +- sqrt2#
Since tan 22.5 is positive, then take the positive answer:
tan (22.5) = - 1 + sqrt2
Answer:
105.25 g
Step-by-step explanation:
The average weight is the sum of the weights divided by the number of pies.
(105 + 105 + 106 + 108 + 108 + 103.5 +102 +104.5) / 8
= 105.25
Answer:
84. What you did is right.
Step-by-step explanation:
A parallellogram's area is b x h. So the equation is 7 x 12=84.
And what I need more information to answer your question.
