A triangle has 3 sides and 3 angles. The triangle involve is an acute triangle. This means that the rest of the angles in the triangle is acute. Acute angles are angles with measurement blow 90 degrees. To solve this problem we use the Sin Law. The ratio of the side and sine of the angle apposite to the side is constant. 10/sin(42) = 12/sin(x). Solve for x.
The answer is 53.41 degrees.
Answer:
need more details
Step-by-step explanation:
what system
1 km = 0.621 mile;
5 km = 0.621 * 5 = 3.105 miles;
31 : 3.105 = 9.9838969 ≈ 9.98 minutes
Answer: C ) 9.98 minutes
Answer:
The size of angle AFE (or Angle F) is 162º.
Step-by-step explanation:
A hexagon's angles add up to 720º. Since there is one line of symmetry (straight down the middle), angle A is the same as angle B; 117º, also known as X. This means angle F is equal to angle C, and angle E is equal to angle D. <em>Angles A and B are to be represented by X. Angles F and C are to be represented by Y. Angles E and D are to be represented by Z.</em> We need to find the remaining sum of the unknown angles: 720 - (117 • 2) = 486º. In the given information, angles BCD (y) is equal to 2 • angle CDE (z). In other words, y = 2z. There are 2y; to convert 2y into z's, we multiply y's equal of z by 2 to get 4z. <u>2y = 4z.</u> Now we can write an equation to solve: (720 - 2x) ÷ (4z + 2z) = z. Where x is 117º. First we solve part 1:
720 - 2(117) = ?
720 - 234 = 486º
Rewrite the equation: 486 ÷ (4z + 2z) = z. That's not how I want to solve it, so I'm rewriting it again as 486 = 4z + 2z. Now to solve it:
Solve for z (Part 2):
486 = 4z + 2z
486 = 6z Combine like terms
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Long division:
<u>081</u>
6 |486
<u>- 0</u>↓
48
<u>- 48</u>↓
06
<u>- 6</u>
0
----------------------------------------------------------------------
<u>81 = z Divide both sides by 6</u>
<u />
Solve for y:
y = 2z
y = 2(81) Plug 81 in for z
<u>y = 162 </u>
Checking my work:
720 = 2x + 2y + 2z
720 = 2(117) + 2(162) + 2(81) 117 = x; 162 = y; 81 = z
720 = 234 + 324 + 162 Simplify
<u>720 = 720 Add</u>
<u />
Woop woop!! We're <em>almost</em> done!
Remember the question is asking us to "work out the size of angle AFE" (or angle F for short). Angle F is represented by y, so we simply look for where we solved for y and see that y(AFE) = 162.
Hope this helps,
❤<em>A.W.E.</em><u><em>S.W.A.N.</em></u>❤
