First we dra a triangle:
To prove that the triangles are similar we have to do the following:
Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:
Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:
With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:
Now that we know that both triangles are similar we can use the following proportion:
this comes from the fact that the ratios should be the same in similar triangles.
From this equation we can find h:
![\begin{gathered} \frac{h}{x}=\frac{y}{h} \\ h^2=xy \\ h=\sqrt[]{xy} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7Bh%7D%7Bx%7D%3D%5Cfrac%7By%7D%7Bh%7D%20%5C%5C%20h%5E2%3Dxy%20%5C%5C%20h%3D%5Csqrt%5B%5D%7Bxy%7D%20%5Cend%7Bgathered%7D)
Plugging the values we have for x and y we have that h (that is the segment CD) has length:
![\begin{gathered} h=\sqrt[]{8\cdot5} \\ =\sqrt[]{40} \\ =\sqrt[]{4\cdot10} \\ =2\sqrt[]{10} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%3D%5Csqrt%5B%5D%7B8%5Ccdot5%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B40%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B4%5Ccdot10%7D%20%5C%5C%20%3D2%5Csqrt%5B%5D%7B10%7D%20%5Cend%7Bgathered%7D)
Therefore, the length of segment CD is:
![CD=2\sqrt[]{10}](https://tex.z-dn.net/?f=CD%3D2%5Csqrt%5B%5D%7B10%7D)
So, first you must find the remaining angle measure. To do this add 25 and 90 then subtract from 180. The remaining angle measure is 65 degrees.
Next, use tangent, cosine, or sine to find the remaining side lengths.
I used sine of 25 which is opposite of hypo. which is sine 25 = y/43.
Multiply both side by 43 and you get y=18.17
Do the same to find x, but use the sine of 65, and you get sine 65 = x/43.
Multiply both sides by 43 and you get x=38.97
Hope this helped!
What is the equivalent value of 1/3×(−15)
Answer: -5x
If we look at our SOHCAHTOA rule:
cos(x) = adj/hyp
The adjacent side of N is 36, and the hypotenuse is 39.
Therefore:
cos(N) = 36 / 39
The probability that a person could not give up cell phone but could give up television can be expressed as the probability of No could give up cell phone and Yes could give up television, P(NnY) = 0.39
<u>From the two way probability table given</u> :
- Let, probability that a person could not give up cell phone = N
- Probability that a person could give up television = Y
The intersection of Y and N = P(Y n N)
- The probability value at the intersection point using the table given ls 0.39
Therefore, the probability of YnN is 0.39
Learn more :brainly.com/question/18153040
