Option D:
Segment DF
Solution:
Let us first define the relationship between the side and angle in triangle.
<u>Relationship between the side and angle in triangle:</u>
- The shortest side is always opposite to the smallest interior angle.
- The largest side is always opposite to the largest interior angle.
To find the largest side in ΔDEF:
Largest angle in ΔDEF is ∠E = 73°
So, the side opposite to 73° is DF.
Therefore, Option D is the correct answer.
Hence the segment DF is the longest side in the ΔDEF.
Answer:
C. 18 cm
Step-by-step explanation:
The ratio of the sides of the triangle shown is 12 : 15 = 4 : 5. We know it is a right triangle, so we know the missing side length completes the ratio
3 : 4 : 5 = 9 : 12 : 15
Half of XY is 9 cm, so the length of the entire chord is 18 cm.
_____
The chord is tangent to the inner circle, so makes a 90° angle with the radius to that tangent point. This tells you that the triangle shown is a right triangle. It also tells you that the short radius bisects the chord. The Pythagorean theorem can be used to find the length of the side not shown (half the chord length).
The unknown side (a) can be found from ...
15² = 12² +a²
225 -144 = a² . . . . . . subtract 12²
81 = a² . . . . . . . . . . . simplify
9 = a . . . . . . . . . . . . . take the square root
The chord length is 2a, so is ...
2(9 cm) = 18 cm . . . . length of chord XY
keeping in mind that perpendicular lines have negative reciprocal slopes, hmmmm what's the slope of that line above anyway,
![\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}\implies \cfrac{2+1}{3}\implies 1 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B-1%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B2%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B2%7D-%5Cstackrel%7By1%7D%7B%28-1%29%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B4%7D-%5Cunderset%7Bx_1%7D%7B1%7D%7D%7D%5Cimplies%20%5Ccfrac%7B2%2B1%7D%7B3%7D%5Cimplies%201%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
so we're really looking for the equation of a line whose slope is -1 and runs through (2,5)
Answer:
m=-4
Step-by-step explanation:
5m-10m=-10m+5m=-(10m-5m)=-5m=20
divide by 5 on both sides, -m=4
miltiply by -1 on both sides, m=-4
namely, how many times does 3/4 go into 3½? Let's firstly convert the mixed fraction to improper fraction.
![\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{2}\div \cfrac{3}{4}\implies \cfrac{7}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{3}\implies \cfrac{14}{3}\implies 4\frac{2}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B7%7D%7B2%7D%5Cdiv%20%5Ccfrac%7B3%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B7%7D%7B~~%5Cbegin%7Bmatrix%7D%202%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%5Ccdot%20%5Ccfrac%7B%5Cstackrel%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%204%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%7B3%7D%5Cimplies%20%5Ccfrac%7B14%7D%7B3%7D%5Cimplies%204%5Cfrac%7B2%7D%7B3%7D)
