Points) Find the angle that maximizeg the area of the isosccles triangle whose legs have length (See figure bolow )...

Find the angle $\theta$ that maximizes the area of the isosceles triangle whose legs have length $\ell$ (Figure 14).

Find the idea of triangle Asian in the figure from figure V C ABC are the Vertex is off triangle co ordinate off. It is minus two coma one coordinate off B is for Come on. One in. Coordinate off sees seven coma food. A geo triangle is half multi play by bass Multiply by height. He had Redick best as a B then lent off a be will be by using distance from love will be minus two comma minus four. Holy square plus one minus one only square. From here we get a big 1 to 6. Hide will be four caressed Morning I for best a be will be. See Victor is according to three. Because cordoning off see is seven common food and coordinate off. He is seven coma. What? From here we get high now. Area will be half multiply by basis six and height is three. Cancel out from here. Redick. Avia, Off Triangle is nine units. We came right here. Nine units

Hello. Um So from our figure we can see that our base B is going to be equal to 3.46 ft and that our altitude or height H. Is going to be equal to 2.55 ft. And we know that the area of a triangle well area is equal to one half base times height, one half B times H. So therefore the area of this triangle is going to be equal to um The area is equal to one half times 3.46 ft Times 2.55 ft, which gives us four about approximately 4.4 and then three times feet gives us beat squared for area. So the area of this triangle is approximately 4.4 ft Squared.

All right. We're asked to find the value of a nice sauce, Elise Triangle that looks like this. And the value of and I saw see, strangled were asked to find the area of a nice sauce. Elise triangle that looks like this. And we use terminology like leg of a nice sauce, please. Triangle. The legs are the two that are the same. And then the vertex is tthe e angle at which the two sides that are the same meat. So if you weren't sure about the terminology, but with the picture, it's easiest. Here we can use a equals 1/2 a B sign of the seat. And if I plug in here, I get 1/2 12 times, 12 times the sign of 45 degrees. And then they want the exact answer here. And so I can do 12 times 12 is 100 and 44 over, too, which is 72. So I have 72 times. This is going to give me rude, too over too. Cancel that you get 36 times a schoolmate of two

So for this problem, we are going to want to find the area of this triangle right here. And we can start by writing down the formula for the area of a triangle. And we know that our area is going to be equal to 1/2 the height of the triangle times the base of that triangle. So our height of our triangle, we can see is going to be from this bottom line here, up to our point C, which we can see a live straight across. So it's gonna be this distance between, uh, of this this line segment right here. This one, and our base is going to be just the distance from A to B. So, uh, since these are straight lines, we can go ahead and just count the units without having to use our distance formula at all. So our base is going to go from our point a right here at negative, too, to point B at four so we can count our units. Leo. 12345123456 units across. So our base is equal to six. I'll go ahead and write that on the side here and for our height again. We said we will start at this dash line here and go up to our black dash line so we can count our unity. And we have 12123 units. So our height is equal to three and we want to find our area. All we have to do is plug in those numbers into our formula. So we get our area is 1/2 times three times six, and when we simplify that we get, our area equals nine.