Here we are given with a triangle with smaller triangles formed due to the altitude on AC. Given:
- AB = 6
- BC = 8
- <ABC = 90°
- BD ⊥ AC
- <ABD =
We have to find the value for sin
So, Let's start solving....
In ∆ADB and ∆ABC,
- <A = <A (common)
- <ABC = <ADB (90°)
So, ∆ADB ~ ∆ABC (By AA similarity)
The corresponding sides will be:
We know the value of AB and to find AC, we can use Pythagoras theoram that is:
AC = √6² + 8²
AC = 10
Coming back to the relation,
In ∆ADB, we have to find sin which is given by perpendicular/base:
Plugging the values of AD and AB,
Simplifying,
And this is our final answer.....
Carry On Learning !
1. First, put the range in order and then divide the set into quarters. In this case, quartiles are between numbers.
<span>83, 85, 89, l 91, 95, 104, l 112, 118, 118, l 125, 134, 138
Q</span>₁ = (89 + 91)/2 = 90
Q₂ = (104 + 112)/2 =108
Q₃ = (118 + 125)/2 = 121.5
Interquartile range (IQR) = Q₃ - Q₁
= 121.5 - 90
IQR = 31.5
2. To find the standard deviation follow the simple steps.
Formula in finding the standard deviation: (see attached file)
Step 1. Work out the simple average of the numbers (mean)
<span><span><u>212 + 249 + 212 + 248 + 239 + 212 + 216 + 234 + 248</u>
</span> 9
= <span><u>2070</u>
</span> 9
mean (</span>μ) = 230
Step 2. Subtract the mean on each number and square the result.
212 - 230 = (-18)² = 324<span>
249 </span>- 230 = ( 19)² = 361<span>
212 </span>- 230 = (-18)² = 324<span>
248 </span>- 230 = (18)² = 324<span>
239 </span>- 230 = (9)² = 81<span>
212 </span>- 230 = (-18)² =324<span>
216 </span>- 230 = (-14)² =196<span>
234 </span>- 230 = (4)² =16<span>
248 </span>- 230 = (18)² =324
Step 3. Add all the squared results and get the mean.
<span><u>2274</u>
</span> 9
Variance = 252.6666667
Step 4. Get the square root of the variance.
√252.6666667
= 15.89549202
Answer:
47.3
Step-by-step explanation:
A triangles angles add up to 180 degrees
At 42.7 and 90 and you get 132.7
Subtract 132.7 from 180 and you get 47.3 degrees.
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