12. Find the angle in degrees, rounded to one decimal. 13. *...

12. Find the angle in degrees, rounded to one decimal. 13. * Find the exact value of cos(sin?¹(24/25)) 14. * Rewrite the expression, cos(tan?¹(x)) as an algebraic expression in x. 15. A 20-ft ladder is leaning against a building. If the base of the ladder is 9 feet from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.) How high does the ladder reach on the building? (Round your answer to the nearest whole number.) 16. The four cases in which we can solve a triangle are: ASA SSA SAS SSS a. In which of these cases can we use the Law of Sines to solve the triangle? (Select all that apply.) b. Which of the cases listed can lead to more than one solution (the ambiguous case)? (Select all that apply.)

Transcript

00:01 Now in question number 12 it has been given that base is equal to 5 unit and hypotenuse is given as 6 unit.

00:13 So we have to calculate theta.

00:16 Now we know that cost theta equals to base divided by hypotenous.

00:23 So that will be 5 divided by 6.

00:29 So we will get 0 .830.

00:34 So, theta will be equals to cos inverse 0 .833 and that is equals to 33 .6 degree.

00:51 So that means the answer for question number 12 will be, theta will be equals to 33 .6 degree.

00:59 So this is the answer for 12.

01:01 Now coming to the question number 13, that is sign we have to find cosass into sine inverse 24 by 25.

01:14 So 24 divided by 25 is 0 .96.

01:25 And if we take sine inverse of that, we will get sine inverse of 0 .96 equals to 73 .74 degree.

01:39 And the cost of this angle, will 73 .74 degree will be 0 .28.

01:47 So the answer for question number 13 is 0 .28.

01:55 Now coming to the question number 14, that is we have to write cost 10 inverse x into as an algebraic expression in x.

02:09 Now let's say there is a triangle.

02:14 Here the height is h, base is one unit and so we can also calculate hypotenous equals to xx2 plus 1.

02:25 And let's say this is theta.

02:28 So theta can be written as, sorry, tan theta can be written as x divided by 1.

02:37 So, theta can be written as tan inverse x, but also this theta can also be written as cos, sorry, or let's say first write, cost theta can also be written as 1 divided by root under 1 plus x square, that is, base divided by hypotenous, is the value of cost theta.

03:02 So from here we can write theta equals to cos inverse 1 divided by root under 1 plus x square.

03:11 So now come to this question that is cost tan inverse x.

03:15 So tan inverse x basically gives here theta.

03:19 So we can write tan inverse x equals to cost theta, where theta is this.

03:26 But we can also replace theta with this value.

03:29 So, we can write cos, where theta can be also written as cos inverse 1 divided by root under 1 plus x square.

03:44 Now we know that this cos and cos inverse will get out of the expression and we will get the final value as equals to 1 by root under 1 plus x square.

04:00 So, we can write cos into tan inverse x equals to 1 by root under 1 plus x square because originally we started from here, cost tan inverse x equals to cost theta and theta can be written as this way and this cost and cost inverse you will get out of this expression.

04:25 And so finally we will get this result.

04:26 So, we can say that the answer for question number 14 is 1 divided by root under 1 plus x square.

04:42 Now coming to the question number 15, it has been given that there is a wall and a 20 feet ladder is leaning against this building or the wall.

04:59 Now the base, the distance from the building to the ladder base is 9 feet away and the length is 20 feet, that is the length of the ladder.

05:14 So we have to calculate the angle of elevation, this theta.

05:18 Now in this triangle, let's say o, a, b, we can write cost theta equals to 9 divided by 20, so, theta will be cos inverse 9 divided by 20...

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